NRLF 


r 


REESE  LIBRARY 

OF  THK 

UNIVERSITY  OF  CALIFORN 


_-n_jT_ji, 


IA. 


A  SYSTEMATIC  TREATISE 


ON 


ELECTRICAL 


MEASUREMENTS 


BY 


HERSCHEL  C.   PARKER,   PH.  B., 


Tutor  in  Physics,    Columbia   University.       Instructor   in   Electrical   Measurements 
Associate  Member  of  the  American  institute  of  Electrical  Engineers. 


NEW  YORK: 
SPON  &  CHAMBERLAIN,  12  CORTLANDT  ST- 

LONDON : 

E.  &  F.  N.  SPON,  LIMITED,  m  STRAND. 

1897, 


• 


Entered  according  to  Act  of  Congress  in  the  year  1897  by 

HERSCHEL  C.  PARKER,  PH.  B. 
in  the  office  of  the  Librarian  of  Congress  at  Washington. 


Press  of  Mcllroy  &  Emmet.  36  Cortlandt  St.,  N.  Y. 


NOTK 


The  present  Treatise  on  Electrical  Measurements  recently 
appeared  as  a  series  of  articles  in  an  electrical  monthly  and  has 
been  bound  in  book  form  with  but  very  little  revision.  It 
should,  therefore,  not  be  judged  as  a  finished  work. 

The  method  of  classification  here  made  use  of  has  been  found 
very  satisfactory  in  several  courses  of  lectures  given  by  the 
writer  to  students  in  Electrical  Engineering  at  Columbia 
University. 


CONTENTS. 


CHAPTER  I.  PAGE 

CLASSIFICATION  OF  ELECTRICAL  MEASUREMENTS 3 

CHAPTER  II. 
GALVANOMETERS  8 

CHAPTER  III. 
Low  RESISTANCE 19 

CHAPTER   IV. 
THE  WHEATSTONE  BRIDGE 28 

CHAPTER  V. 
SPECIFIC  RESISTANCE  AND  GALVANOMETER  RESISTANCE 38 

CHAPTER  VI. 
COMPARISON  OF   STANDARDS   AND    CALIBRATION    OF   BRIDGE 

WIRE  AND  RHEOSTAT 41 

CHAPTER   VII. 
HIGH  RESISTANCE , 46 

CHAPTER  VIII. 
INSULATION 49 

CHAPTER   IX. 
RESISTANCE  OF  TELEGRAPH  LINES,  CABLES,  ETC 55 

CHAPTER  X. 
LOCALIZATION  OF  FAULTS 58 

CHAPTER  XI. 
RESISTANCE  OF  BATTERIES   AND  ELECTROLYTES 63 

CHAPTER  XII. 
INCANDESCENT  LAMPS,  DYNAMO  RESISTANCE,  ETC 68 


yi  CONTENTS. 

CHAPTER  XIII. 
DETERMINATION  OF  THE  OHM,  CONSTRUCTION  OF  STANDARDS, 

ETC 70 

CHAPTER  XIV. 
MEASUREMENT    OF    E.    M.    F.    OF    BATTERIES   AND    DIRECT 

CURRENTS 73 

CHAPTER  XV. 
E.  M.  F.  OF  ALTERNATING  CURRENTS,  VERY  HIGH  E.  M.  F. 

AND  VERY  Low  E.  M.  F 81 

CHAPTER  XVI. 
CALIBRATION  OF  VOLTMETERS,  AND  STANDARDS  OF  E.  M.  F.     86 

CHAPTER  XVII. 
MEASUREMENT  OF  CURRENT 89 

CHAPTER-  XVIII. 
MEASUREMENT  OF  ENERGY  AND  QUANTITY. TOO 

CHAPTER  XIX. 
MEASUREMENT  OF  CAPACITY 103 

CHAPTER  XX. 
INDUCTANCE 108 

CHAPTER  XXL 
MEASUREMENTS  OF  EFFICIENCY 112 

CHAPTER  XXII. 
MAGNETIC  DETERMINATIONS 114 

INDEX..  u8 


INTRODUCTION. 


AN  ACCURATE  knowledge  of  electrical  measurement,  to  the 
electrical  engineer  as  well  as  the  physicist,  is  of  the  first 
importance. 

It  is  a  branch  of  science  where  engineering  and  physics  meet. 

There  appears,  however,  in  many  instances,  to  be  a  lack  of 
uniformity  in  the  methods  employed.  Indeed,  it  almost  seems 
as  if  there  were  two  schools  of  electrical  measurement.  But 
this  is  probably  due,  to  some  extent  at  least,  to  the  lack  of  a 
proper  co-ordination  and  classification  of  the  subject. 

New  methods  of  practice  have  rapidly  developed,  and  im- 
proved instruments  are  constantly  coming  into  use,  so  that  it  is 
not  strange  if  there  be  a  little  confusion. 

Thus  we  may  find  a  text-book  that  is  almost  perfect  as  far  as 
resistance  work  is  concerned,  but  deficient  with  regard  to  E.M.F. 
or  current,  describing  at  length  obsolete  methods  and  entirely 
omitting  many  of  the  best  ones.  So  that  often  the  student  may 
be  compelled  to  consult  a  great  number  of  standard  works  and 
supplement  this  by  long  personal  observation  to  obtain  even  a 
fair  comprehension  of  the  practical  methods. 

The  subject,  it  seems  to  the  writer,  should  be  attacked  in  the 
most  systematic  manner  and  the  classification  thoroughly 
worked  out.  Indeed,  classification  and  knowledge  are  very 
nearly  synonymous  terms. 

What  follows  is  offered  as  an  example  of  such  a  method  of 
treatment. 

It  seemed  advisable  to  make  the  classification  fairly  complete^ 
and  then  to  clearly  point  out  the  most  desirable  methods  or 
those  applicable  to  any  particular  case. 

Of  course,  there  are  many  omissions  and  possibly  errors  ;  but 

i 


2  INTRODUCTION. 

it  is  hoped  that  it  will  facilitate  the  acquirement  of  a  working 
knowledge  of  the  subject  by  students  of  electrical  engineering. 
In  the  text  of  the  treatise,  free  use  has  been  made  of  the 
standard  works,  especially  "  Kempe's  Hand-book  of  Electrical 
Testing,"  but  it  is  also  believed  that  a  considerable  amount  of 
new  material  is  presented. 


CHAPTER  I. 


CLASSIFICATION  OF  ELECTRICAL  MEASUREMENTS 


Low    RESISTANCE. 


RESISTANCE. 

1.  Thomson's  Double  Bridge.* 

2.  Differential  Galvanometer.* 

3.  Projection  of  Potentials. 

4.  Fall  of  Potential. 

5.  Potentiometer. 

6.  Carev  Foster's  Method. 


WHEATSTONE 


BRIDGE. 


SPECIFIC 

RESISTANCE 


MEDIUM  RESISTANCE. 


Wire  Bridge.. 

(Variable  Ratio  ) 


f  Straight  (Metre). 
J  Circular  (Kohlrausch). 
j  Parallel  (Poggendorff). 
[Direct  Reading  (Kirchhoff). 


o/  -j    r   •/  (  Five  Arc  (Cushman).* 

Sltde  Cotl \  Quadruplex(Muirhead) 

(Variable  Ratio.)          |  Duplex  (Varley). 


(  P.  O.  Bridge.* 
."  "1  Conductivity  Balance. 


COMPARISON  OF 

STANDARDS 


j  Carey  Foster's  Method.* 
.   (  Substitution  in  the  Bridge. 


CALIBRATION... 


Bridge    Wire . . . 


(  Comparison  with  Rheostat  (Po- 
tentiometer Method.)  * 
-|  Carey  Foster's  Method. 
|   Double  bridge. 
I   Differential  Galvanometer. 


Rheostat ]  Substitution  in  the  Bridge. 


GALVANOMETER 

RESISTANCE. 


P.  O.  Bridge.* 
Thomson's  Method. 
y>>  Deflection. 


HIGH  RESISTANCE. 


Slide  Coil  Bridge.* 
Potentiometer  Method. 
Deflection  Method.* 
Loss  of  Charge. 

3 


INSULATION. 


ELECTRICAL  MEASUREMENTS. 

i.  Insulite.—"  Specific  Insulation." 
Short  Lengths. 

ft 


2.  Insulated 

Wires.  \ 


3.  Aerial    Wires. 


r  ,  ,     (  Single  Core. 
^aDie>  (  Multiple  Core. 


j  Loss  of  charge.* 
Joint  Testing.  \  Accumulation. 
(  Electrometer. 


RESISTANCE  OF 

TELEGRAPH  LINES, 

CABLES,  ETC. 


LOCALIZATION  OK 
FAULTS. 


1.  P.O.  Bridge. 

2.  Loop  Test |  £ 

3.  Equilibrium. 

4.  Mance's  Method. 

5.  Equal  Deflection. 

1.  Complete  Fault  in  Insulation. 

2.  Partial        "       "  (Earth  Resistance.) 

3.  Variable     "       "  "  (Polarization  or  Ca- 

ble Current.) 

4.  Fault  plus  E.  M.  F.  (Earth  Current.) 

5.  Fault  in  Conductor. 

6.  Faults  of  High  Resistance. 


BATTERY  RESIS- 
TANCE. 


RESISTANCE  OF 
ELECTROLYTES. 


,  Fall  of  Poten.  (  ^ 
ttal* j  Volt 


•{  2.  Added 
tance 


Resis- 


Voltmeter.* 

Tangent  Galvanometer. 
•  *A  Deflection. 


3.  Mance's  Method. 
„  4.  Current  and  E.  M.  F* 

(  Constant  Current. 

\  Alternating  Current* 


INCANDESCENT 
LAMPS,   "  DYNAMO 
RESISTANCE,"  ETC. 


Fall  of  Potential. 
Current  and  E.  M.  F. 
Ohmmeter. 


DETERMINATION  OF  THE  OHM. 


ELECTROMOTIVE  FORCE. 


BATTERIES  AND 
DIRECT  CURRENTS. 


Resistance  \ 

'•* i 


Deflection  and  Resistance. 
Deflection. 
Resistance. 


Wheatstone's  Method. 
Lums  den's 
Condenser  "  * 


Potentiometer.  * ... 


Five  Arc  (Cushman.) 

8uadruplex  (Muirhead.) 
uplex  (Varley.) 


Current  and  Resistance. 
Electrometer. 
Voltmeter* 


CLASSIFICATION. 


ALTERNATING 

CURRENTS. 


Quadrant. 
,  Multicellular.* 

Electrometer \   Electrostatic  Volt-  j  Thomson's. 

meter.*/  Weston's. 
Low  Reading. 

i  Siemens' 
Weston's*  (Alternating  Current 
Voltmeter.) 

Caloric  Voltmeter  (Cardew's.)* 

Attraction     Volt-  j  Evershed's. 
meters 1  Magnetic  Vane,  etc. 


(  Electrostatic  Voltmeter. 
VERY  HIGH  E.  M  F.  \  Absolute  Electrometer. 

(  Striking  Distance  of  Spark. 

(  Galvanometer* 
VERY  Low  E.  M.  F.  \   Voltmeter* 

(  Capillary  Electrometer  (Lippmann's.) 


STANDARDS  OF 

E 


.{ 

?M  F    I  Checking  by  Current  and  Resistance. 


CURRENT. 


DIRECT  CURRENTS. 


*  **  B       j  v*    (  Di 

,.  M.  P.  and  Ke-  J  Di 

stance  ..........    j  Bri 


E. 

sistance 


Direct  Method. 

Differential  Method  (Cardew's.) 

Bridge  Method  (Kempe's.) 


D    n      *,J  r?,e,-c 
P.  D.   and  Rests- 

tance  .......... 


Direct    Deflection    Method. 
Equilibrium  Method. 
potentiometer    " 
Voltmeter  "* 

Galvanometer    "* 


Tangent  Galvanometer. 


Ammeter.* 


f  D 
C 


Dy 
Cu 


namometer. 


urrent  Balance  (Thomson's.) 


ALTERNATING^   ^  Attraction      Am-  (  Evershed's,  Schuckert's,  etc. 
I  meters ( 

\  Calorimetrtc  Methods. 
CALIBRATION  OF  AMMETERS. 
ABSOLUTE  DETERMINATION  (Tangent  Galvanometer.) 


ELECTRICAL  MEASUREMENTS. 


Voltmeter  and  Ammeter. 

( 
QUANTITY. 


(    Voltameter, 

r ..  -J   "Meters" 

(  Ballistic  Ga 


Galvanometer. 


CAPACITY. 


Direct  Deflect  ton* 
Divided  Charge 


M™.... 
ABSOLUTE  DETERMINATION  (Ballistic  Galvanometer.) 

INDUCTANCE. 
BRIDGE  METHOD  (Maxwell's.) 

SECOHMMETER  j    With  Standard. 

METHOD.  \    Withou'     4' 

CONDENSER  j  Deflection. 

METHOD.  \  Zero. 

CALCULATION. 
[IMPEDANCE.] 


f  Cells. 
\  Lamps. 

EFFICIENCY ^  Motors. 

Transformers. 
[  Dynamos. 


Field  (OC) 

Intensity  of  Magnetization 

/  &  \ 

Permeability  (p   --  —  1 
MAGNETIC  .  \  3C/ 

DETERMINATIONS,   j  /  3  \ 

Susceptibility   Ir^j 
VJC/ 

I  Hysteresis. 

\  Magneto-Motive  Force. 

^  Reluctance. 


CLASSIFICATION.  7 

REMARKS. 

In  the  above  classification  it  is  not  attempted  to  give  the  vari- 
ous methods  in  the  order  of  their  relative  merit,  but  rather  ac- 
cording to  their  logical  sequence. 

What  are  believed  to  be  the  superior  methods,  or  those  especi- 
ally applicable  in  any  given  case,  are  indicated  by  stars. 

In  the  classification  of  resistance  measurements  it  was  thought 
advisable  to  give  the  different  forms  of  the  Wheatstone  Bridge. 
It  also  seemed  best  to  classify  the  different  cases  of  "  Insula- 
tion "  and  those  that  might  occur  in  the  "  Localization  of 
Faults." 

The  determination  of  "  Energy  "  and  of  u  Quantity  "  so  closely 
approximates  the  measurement  of  current  that  they  appear  to 
belong  as  sub-headings  under  that  subject. 

"  Impedance  "  is  given  as  a  special  application  of  the  meas- 
urement of  "  Inductance." 

Under  "  Efficiency  "  are  given  several  special  cases. 

To  complete  the  subject,  a  number  of  Magnetic  Determina- 
tions are  added,  for  there  certainly  should  be  no  fixed  line  drawn 
between  electrical  and  magnetic  measurements,  considering  the 
present  state  of  electrical  science. 


CHAPTER  II. 
GALVANOMETERS. 


Tangent. 
Astatic. 

j  Single  Coil. 

MOVABLE  MAGNET-  J    Thomson -j  Duplex. 

ic  SYSTEM.          ]  (  Quadruplex. 

Aperiodic. 
Differential. 
Ballistic. 


<\ 


Weston  Pattern  (Portable  ) 

MOVABLE  COIL • 

Ayrton  &*  j  Aperiodic. 

Mather  Pattern..  \  Ballistic. 
Rowland    ~~~** 
Electro-Magnet  Pattern. 

GENERAL. 

Figure  of  Merit.  —  By  the  "Figure  of  Merit"  is  meant  the 
strength  of  current  required  to  produce  a  deflection  of  one  scale 
division,  or  the  resistance  that  must  be  introduced  into  the  cir- 
cuit to  reduce  the  deflection  to  one  scale  division  with  a  p.  D.  of 
one  volt. 

All  the  conditions  should  be  specified,  such  as  the  distance  of 
the  scale  from  the  galvanometer,  width  of  scale  divisions  *  and 
time  of  vibration  of  galvanometer. 

(  Deflection  =  250  scale  divisions  (joV^r  shunt.) 
Example  :  •<  P.  D.  =  2.5  volts. 

(  Resistance  =  100,000  ohms. 

Figure  of  Merit  =  I00>000  ^o  x  r>000  =  '  X  io-»  amperes. 

or  i  X  i o10  ohms,  that  is  .0001   micro-amperes,  qr  10,000  meg- 
ohms. 

Sensitiveness. — This  term  may  be  employed  to  indicate  the  P.  D. 
across  the  galvanometer  terminals  necessary  to  give  a  deflection 
of  one  scale  division.  Since  E  =  C  R,  it  may  be  obtained  by 

*  Unless  otherwise  specified  it  is  assumed  that  a  mm.  scale  is  used  at  the  distance  of  a  metre 
from  the  galvanometer  mirror. 


GALVANOMETERS.  $ 

multiplying  the  figure  of  merit  by  the  resistance  of  the  galvan- 
ometer. 

Thus,  if  the  galvanometer  in  the  above  example  had  a  resist- 
ance of  10,000  ohms,  its  "  Sensitiveness  "  would  be  .0001  micro- 
ampere X  10,000  =  i  micro- volt. 

In  the  measurement  of  low  resistance  it  is,  of  course,  desirable 
to  have  a  galvanometer  of  the  maximum  "  efficiency."  Usually, 
galvanometers  of  low  resistance  have  a  greater  efficiency  than 
those  of  high  resistance,  but  the  figure  of  merit  increases  with 
the  number  of  turns,  and  consequently  high  resistance  galvan- 
ometers have  a  greater  figure  of  merit.  In  the  measurement  of 
high  resistance  and  insulation  the  galvanometer  resistance  has 
but  little  effect  on  the  current,  and  hence  it  is  best  to  employ  a 
galvanometer  with  the  maximum  figure  of  merit. 

Shunts. — In  order  to  vary  the  sensitiveness  of  galvanometers, 
a  portion  of  the  current  is  deflected  by  a  resistance  in  parallel 
with  the  galvanometer.  The  value  of  this  shunt  is  given  by  the 
formula :  e  _  •  „  i 

O   —    Lr    X    

n—  i, 
where  S  =  resistance  of  shunt,  G  =  resistance  of  galvanometer, 

and  1  =  the  portion  of  the  current  received  by  the  galvanome- 

n 

ter,  (that  is,  the  amount  the  galvanometer  deflection  is  reduced 
to,  where  such  deflection  is  proportional  to  the  current.) 

Example  :    in.i  =  1000  X  

10 — i 

In  this  case  the  resistance  of  a  one-tenth  shunt  for  a  1000  ohm 
galvanometer  must  be  in.i  ohms. 

When  the  resistance  in  the  main  circuit  is  comparatively  low, 
the  use  of  a  shunt  reduces  the  resistance  of  the  entire  circuit  an 
appreciable  amount  and  introduces  a  certain  error  in  the  meas- 
urement unless  a  compensating  resistance  is  added. 

The  formula                  cl        ^       n  —  i 
o     —  (JT  X    


gives  the  value  of  this  resistance.     In  the  above  example  it 
would  be  ooo  ohms    /  f  10 

(9°°  =  '>co°  x  -F 

Errors. — With  a  reflecting  galvanometer  and  a  tangent  scale, 
the  beam  of  light  is  deflected  through  twice  the  angle  that  the 
mirror  is  turned.  In  an  observation  where  two  deflections  are 
taken,  the  error  in  assuming  that  the  ratio  of  the  tangents  of 
twice  the  angles  is  the  same  as  the  ratio  of  the  tangents  of  the 
angles  may  amount  to  one  per  cent,  or  over  where  the  ratio 
is  greater  than  six  to  one. 


to 


ELECTRICAL  MEASUREMENTS. 


The  formula  for  the  induction  is  : 

--/): 


c,  :  cz  ::  d,  (V/8  +  tf  —  /)  :  4  (V**  +  4  — 
where  d^  d%,  represent  the  two  deflections;  cly  cz,  the  ratios  of  the 
two  currents,  and  /,  the  distance  from  the  scale  to  the  mirror  in 
scale  divisions. 

The  error  of  observation  where  two  deflections  are  taken,  is 
increased  the  more  widely  the  deflections  differ.  The  formula  is: 


T  = 


—  X  ioo 
m 


X    (i  +«) 


T  =  percentage  error  of  the  determination,  —  =  error  of  observ- 

m 

ation  in  scale  divisions,  d  =  first  deflection,  n  =  ratio  of   first 
deflection  to  the  second.     Example  : 


250 

From  the  above  considerations  and  also  on  account  of  possible 
variations  in  the  E.  M.  F.  during  experiment,  it  is  apparent  that 
zero  methods  are  preferable.  When  deflection  methods  are 
employed  it  is  often  practicable  to  so  vary  the  P.  D.  that  the  two 
deflections  may  be  nearly  equal.  The  ratio  of  the  differences 
of  potential  is  then  used  in  the  calculation. 

Angle  of  maximum  sensitiveness.  Where  the  strength  of  current 
and  consequently  the  deflections  are  proportional  to  the  tangents 
of  the  angles,  the  galvanometer  has  the  greatest  sensitiveness 
when  the  needle  makes  an  angle  of  45°  with  the  coil.  With  a 
reflecting  galvanometer,  the  angle  of  maximum  sensitiveness  is 
the  largest  angle  that  can  be  obtained,  since  the  angle  of  deflec- 
tion is  but  a  very  few  degrees  and,  therefore,  the  true  maxknum 
angle  can  never  be  obtained. 

TANGENT  GALVANOMETER. 

In  this  form  of  galvano- 
meter, a  short  magnetic  needle 
is  centrally  placed  within  a 
coil  of  wire  of  large  radius  as 
shown  in  Fig.  i.  The  needle 
may  carry  a  pointer  moving 
over  a  graduated  circle,  or  the 
deflections  can  be  read  by 
means  of  a  mirror  and  tele- 
scope and  scale,  or  lamp  and 
scale. 
FIG-  *•  If  the  influence  of  the  coil 


GALVANOMETERS. 


ii 


*  C 


on  the  needle  is  the  same  whatever  angle  the  needle  makes  with 
it,  then  the  strength  of  the  current  circulating  in  the  coil  is  di- 
rectly proportional  to  the  tangent  of  the  angle  of  deflection. 

Theoretically,  to  obtain  this  result,  the  magnet  should  be  a 
mere  point,  but  practically  it  is  sufficient  for  the  coil  to  be  about 
ten  times  as  large  in  diameter  as  the  length  of  the  needle. 

This  instrument  furnishes  a  most  convenient  means  for  the 
comparison  of  current  strengths,  and  is  of  the  greatest  interest  on 
account  of  its  employment  in  the  absolute  measurement  of  cur- 
rent and  consequently  in  the  absolute  determination  of  the  ohm. 

The  perfection  of  the  ammeter,  however,  and  the  accuracy 
and  facility  with  which  current  may  be  measured  by  determin- 
ing the  P.  D.  across  a  shunt,  render  the  tangent  galvanometer  of 
far  less  importance  than  formerly  to  the  electrical  engineer. 

ASTATIC  GALVANOMETER. 

This  instrument  is  of  very 
simple  construction  and  is 
quite  sensitive.  It  is  especially 
adapted  for  use  with  zero 
methods  or  may  be  employed 
as  a  sine  galvanometer. 

It  consists  of  an  astatic  pair 
of  needles  of  any  convenient 
length  suspended  by  a  fibre 
arranged  as  in  Fig.  2  ;  one 
needle  turns  within  the  coil 
while  the  other  moves  above  it. 
If  the  coil  is  made  to  rotate  and  the  angle  of  rotation  meas- 
ured, then  when  a  current  is  sent  through  the  galvanometer  if 
the  coil  be  turned  until  it  is  parallel  with  the  needles,  that  is,  if 
the  needles  are  again  brought  to  zero,  the  current  is  propor- 
tional to  the  sine  of  the  angle  of  rotation.  This  is  independent 
of  the  size  or  shape  of  the  coil  or  the  length  of  the  needles. 

THOMSON  GALVANOMETER. 

The  limits  in  the  range  of  electrical  measurement  are  usually 
fixed  by  the  sensitiveness  of  the  galvanometer. 

The  highest  figure  of  merit,  and  perhaps  the  greatest  effi- 
ciency may  be  obtained  with  the  Thomson  galvanometer. 

The  magnetic  system  is  astatic  and  is  formed  of  a  number  of 
small  light  magnets,  usually  pieces  of  watch-spring. 

One  set  of  these  magnets  is  attached  to  the  back  of  a  small 
mirror,  while  another  set  is  fixed  to  a  light  aluminium  vane  (Fig.  3) 


^/VVW — I    ' — VWW 


FIG.    2. 


12 


ELECTRICAL  MEASUREMENTS. 


The  upper  set  of  magnets  moves  in  the 'centre  of  a  large  coil  of 
wire  of  many  turns,  while  the  lower  set  is  beneath  the  coil. 
This  coil  consists  of  two  portions,  and  is  hinged  so  that  it  may 
easily  be  opened  and  the  magnetic  system  put  in  place.  The 
high  resistance  galvanometers  are  usually  furnished  with  two 
coils,  and  the  more  recent  instruments  with  four  coils.  There 
is,  of  course,  a  set  of  magnets  for  each  coil,  and  by  this  means 
the  magnetic  moment  and 
number  of  turns  may  be 
greatly  multiplied.  (Fig.  4.) 
The  entire  magnetic  system 
is  suspended  by  means  of  the 
very  finest  fibre,  either  of  silk 
or  quartz. 

The   galvanometer   is  also 


FIG.  3. 


%FIG.  4. 


provided  with  a  field  magnet.     This  magnet  is  used  to  neutral- 
ize the  earth's  field,  and,  being  nearer  the  upper  set  of  magnets 
than  the  others,  it  also  acts  as  a  directing  or  controlling  magnet. 
The  needles  being  very  small,  and  each  set  being  placed  in 


GALVANOMETERS.  13 

the  axis  of  a  large  coil  of  wire  which  completely  surrounds  it, 
the  tangents  of  the  deflections  are  approximately  directly  pro- 
portional .to  the  strength  of  the  currents  producing  them. 

Since  the  deflections  are  read  by  means  of  a  reflected  beam 
of  light,  the  angle  through  which  this  beam  of  light  turns  will 
be  twice  the  angle  through  which  the  mirror  turns,  and,  conse- 
quently, the  deflections  will  be  proportional  to  the  tangents  of 
twice  the  angles. 

If,  however,  the  deflections  to  be  compared  are  both  small,  or 
if  they  do  not  differ  greatly,  these  deflections  may  be  taken  as 
proportional  to  currents  producing  them. 

Considerable  care  is  required  in  setting  up  the  galvanometer. 


FIG.   5. 


FIG.  6. 


A  position  should  be  selected  as  free  from  vibrations  and  mag- 
netic disturbances  as  possible,  and  all  torsion  should  be  carefully 
removed  from  the  fibre. 

The  magnetic  system  is  usually  not  quite  astatic,  and  if  the 
field  magnet  is  removed,  will  set  in  the  magnetic  meridian. 
The  field  magnet  should  then  be  lowered  until  it  just  neutral- 
izes the  earth's  field.  This  is  shown  by  the  magnetic  system 
being  in  unstable  equilibrium.  The  control  magnet  is  then 
raised  slightly  above  this  position. 

Two  control  magnets  are  sometimes  employed  to  render  the 
field  more  uniform. 


i4  ELECTRICAL  MEASUREMENTS. 

The  scale  should  be  placed  parallel  to  the  mirror. 

The  high  resistance  galvanometers  are  wound  with  a  resist- 
ance varying  from  3,500  ohms  to  100,000  ohms,  and  as  great  a 
figure  of  merit  as  100,000  meg-ohms  may  be  obtained.  This 
form  of  instrument  is  extremely  useful  in  insulation  work. 

The  low  resistance  galvanometers  are  extraordinarily  sensitive 
but  are  also  very  easily  affected  by  thermal  currents,  so  that  it 
is  sometimes  found  advisable  to  use  some  form  of  D'Arsonval 
galvanometer  for  low  resistance  determinations. 


FIG.  7. 


APERIODIC  GALVANOMETER. 

In  this  galvanometer  a  large  bell  magnet  is  employed.  This 
magnet  is  enclosed  between  massive  plates  of  copper,  and  hence 
when  set  in  motion  it  induces  powerful  Foucault  currents  in  the 
copper  which  quickly  bring  the  magnet  to  rest.  »(Figs.  5  and  6.) 

Moreover,  slight  changes  in  the  surrounding  magnetic  field 
seem  to  produce  but  little  effect  on  this  form  of  galvanometer, 
and  a  rather  high  figure  of  merit  may  easily  be  obtained  even 
where  no  great  care  has  been  exercised  in  its  construction. 


GALVANOMETERS.  15 

DIFFERENTIAL  GALVANOMETER. 

A  galvanometer  may  be  made  differential  by  winding  two 
wires  on  the  same  coil  or  by  the  use  of  two  coils,  and  then  send- 
ing the  current  through  in  opposite  directions.  It  is  adjusted 
by  sending  the  same  current  through  each  coil  and  adding  re- 
sistance to  one  of  the  coils  until  no  deflection  is  produced. 
Where  two  coils  are  employed,  a  rough  adjustment  may  be 
made  by  moving  one  of  the  coils.  It  is  always  better,  however, 
to  make  the  final  adjustment  by  the  addition  of  resistance. 

The  coils  of  a  Thomson  galvanometer  may  be  connected  dif- 
ferentially. 

The  differential  galvanometer  is  useful  in  the  measurement 
of  low  resistance. 

BALLISTIC  GALVANOMETER. 

For  certain  determinations  a  galvanometer  with  a  long  period 
of  vibration,  a  large  moment  of  inertia,  and  with  but  very  little 
decrement  is  required. 

One  of  the  standard  forms  of  this  instrument  is  shown  in  the 
diagram.  (Fig.  7.) 

Four  bell  magnets  are  employed,  a  coil  of  high  resistance,  a 
control  magnet  and  a  directing  magnet.  It  is  desired  to  give 
the  moving  magnetic  system  considerable  weight  and  yet  have 
the  air  resistance  as  little  as  possible. 

The  mirror  used  should  be  very  small,  and  the  suspending 
fibre  extremely  fine  and  without  torsion. 

This  form  of  galvanometer  is  exceedingly  sensitive  to  vibra- 
brations  and  changes  in  the  magnetic  field.  The  deflections  are 
controlled  by  means  of  a  check  coil  placed  near  the  instrument. 

THE  D'ARSONVAL  GALVANOMETER. 

The  radical  difference  between  this  form  of  galvanometer  and 
those  previously  described,  is  that  here  the  coil  is  movable  and 
the  magnets  are  fixed  as  shown  in  Fig.  8.  A  very  intense  field 
is  obtained  by  the  combination  of  several  horse-shoe  magnets 
having  a  soft  iron  core  or  a  compound  magnet  placed  between 
their  poles. 

In  this  space  moves  the  rectangular  coil  wound  on  a  thin  cop- 
per or  silver  frame.  The  Foucault  currents  induced  in  this 
frame  render  the  galvanometer  almost  aperiodic.  The  resisting 
force  is  the  torsion  of  the  suspending  wires.  Consequently, 
assuming  the  field  to  be  uniform,  the  currents  flowing  through 
the  coil  are  directly  proportional  to  the  angular  deflection. 


16 


ELECTRICAL  MEASUREMENTS. 


WA/VW 


Hence,  for  accurate  work  in 
deflection  methods,  a  circular 
scale  should  be  employed  or  the 
tangential  deflections  reduced 
to  the  corresponding1  angles.  ' 

On  account  of  the  great 
strength  of  field,  this  galvanom- 
eter is  scarcely  effected  by  con- 
siderable magnetic  changes, 
even  in  its  immediate  vicinity. 
The  coil  is  usually  wound  to 
•about  100  ohms,  but  a  higher 
resistance  may  be  used  when 
desired.  The  figure  of  merit 
that  may  be  obtained,  expressed 
in  megohms,  is  usually  some- 
what less  than  the  galvanometer 
resistance  in  ohms. 

For  nearly  the  whole  range  of 
electrical  measurement,  this  gal- 
vanometer is  probably  the  most  satisfactory  one  that  can  be  em- 
ployed. 

When  the  metallic  frame  is 
not  used,  the  decrement  be- 
comes very  small  ;  and  since  the 
weight  of  the  coil  is  consider- 
able, the  moment  of  inertia  is 
large.  That  is,  the  conditions  of 
a  ballistic  galvanometer  are  ful- 
filled. The  moment  of  inertia 
may  be  still  further  increased  by 
adding  a  weight  to  the  coil.  The 
coil  may  be  brought  to  rest  by 
means  of  a  short  circuiting  key. 
Westcn  Pattern. — If  the  coil, 
instead  of  being  suspended  by 
a  wire  turns  in  jeweled  bearings, 
the  current  being  lead  in  by 
delicate  watch-springs  (Fig.  9)  ; 
and  if  the  horse-shoe  magnet  or 
magnets  be  placed  horizontally, 
the  coil  having  an  oblique  posi- 
tion between  the  poles,  the  gal-  FIG.  9. 


GALVANOMETERS.  17 

vanometer  is  then  of  the  Weston  pattern.  This  form  of  instru- 
ment is  generally  used  in  combination  with  a  low  shunt  resistance 
or  a  high  series  resistance  and  then  constitutes  the  well-known 
Weston  ammeter  or  Weston  voltmeter.  Without  these  auxiliary 
resistances,  however,  it  is  one  of  the  very  best  forms  of 
D' Arson val  galvanometer.  The  sensitiveness  is  almost  as  great, 
while  it  is  far  more  compact  and  portable  than  the  ordinary 


/wvv h 


FIG.  IO. 

galvanometer.     Besides  this,  the  angular  deflections  are  accur- 
ately proportional  to  the  currents  producing  them. 

Ayrton  and  Mather. — In  this  form  of  galvanometer  (Fig.  10)  a 
large  number  of  circular  magnets  are  placed  horizontally,  the 
poles  being  brought  very  near  together.  In  this  small  space  is 
suspended  a  long-  narrow  coil.  The  coil  carries  alight  metallic 


i8  ELECTRICAL  MEASUREMENTS. 

sheath  where  aperiodicity  is  desired,  but  is  without  the  sheath 
when  used  ballistically. 

The  coil  may  be  wound  to  as  high  a  resistance  as  4,000  ohms, 
and  a  figure  of  merit  of  over  i,coo  meg-ohms  may  be  obtained. 

This  is  probably  the  best  form  of  ballistic  galvanometer  and 
may  also  be  employed  in  ordinary  insulation  work. 

Rowland. — The  Rowland  D' Arson val  galvanometer  has  an  el- 
liptically  shaped  permanent  magnet  enclosed  between  two  faces 
of  sheet  brass,  thus  forming  a  closed  space  in  which  the  coil 
swings.  The  coil  is  provided  with  a  large  mica  vane  for  damp- 
ening its  vibrations. 

The  pole  faces  of  the  magnet  are  so  shaped  that  the  deflec- 
tions, as  read  with  a  telescope  or  lamp  and  scale,  are  said  to  be 
exactly  proportional  to  the  current  passing. 

The  coil  may  be  given  a  resistance  of  1,500  ohms  and  a  figure 
of  merit  of  500  meg-ohms  obtained. 

Electro- Magnet  Pattern. — The  strength  of  field,  and  conse- 
quently the  sensitiveness  of  the  galvanometer  may  be  increased 
by  the  use  of  electro-magnets.  This,  however,  is  only  necessary 
in  special  cases  of  research  work. 

Conclusions. — From  the  above  considerations  it  is  evident  that 
the  Thomson  galvanometer,  having  the  highest  figure  of  merit 
and  the  greatest  sensitiveness  is  the  most  desirable  for  either  very 
high  or  very  low  resistance  determinations.  In  certain  cases  of 
low  resistance  work,  however,  on  account  of  thermal  currents, 
a  D'Arsonval  galvanometer  may  prove  preferable.  For  all  or- 
dinary measurements  a  D'Arsonval  galvanometer  is  recom- 
mended. For  the  determination  of  high  insulation  it  is  best  to 
employ  a  Thomson  high  resistance  galvanometer. 


CHAPTER  III. 
Low  RESISTANCE. 


f  Thomson's  Double  Bridge  * 

Differential  Galvanometer* 
\  Projection  of  Potentials. 
j  Fall  of  Potential. 
\  Potentiometer 
[  Carey  Foster's  Method. 

Low  resistance  is,  of  course,  a  relative  term  ;  but  it  is  here 
used  to  indicate  resistances  too  small  to  be  accurately  determined 
by  the  ordinary  Wheatstone  bridge  methods.  For  most  re- 
sistance measurements,  an  accuracy  of  about  one  per  cent,  is 
desirable.  That  is,  if  .01  ohm  is  to  be  measiired,  it  requires  the 
determination  to  be  made  to  .0001  ohm.  But  contact  resistances 
are  an  unknown  variable,  and  may  easily  introduce  an  error  as 
great  as  the  last  named  figure. 

Since  the  effect  of  these  contact  resistances  can  never  be  en- 
tirely eliminated  with  the  Wheatstone  Bridge,  the  upper  limit  of 
low  resistance  may  be  placed  at  about  .01  ohm. 

It  is  true  that  there  is  a  form  of  Wheatstone  Bridge  that  reads 
to  .00000 1  ohm,  but  measuring  to  a  millionth  of  an  ohm  and 
reading  to  a  millionth  of  an  ohm  are  very  different  affairs. 

In  most  of  the  special  methods  described,  the  effect  of  contact 
resistance  is  practically  eliminated. 

It  should  also  be  understood  that  when  a  measurement  is 
made  to,  say,  i  x  io~7  ohm,  the  entire  resistance  is  not  much 
more  than  i  x  io~*  ohm.  For  it  is  hardly  possible  in  low  re- 
sistance work  to  measure  better  than  .  i  per  cent,  under  the  most 
favorable  conditions,  on  account  of  temperature  coefficients  and 
thermal  effects. 

The  measurement  of  such  extremely  low  resistances  is  made 

E> 

possible  by  Ohm's  law,  C  =  -  . 

R 

One  of  the  limiting  conditions  is  the  sensitiveness  of  the 
galvanometer,  and  the  galvanometer  deflections  are  approxim- 
ately proportional  to  the  current.  The  current,  however,  is  in- 
versely proportional  to  the  resistance. 

Hence,  the  lower  the  resistance,  the  greater  the  current  for 


20 


ELECTRICAL  MEASUREMENTS. 


any  given  p.  D.  That  is,  the  smaller  the  resistance  in  circuit, 
the  lower  the  limit  of  the  measurement  becomes. 

But,  of  course,  there  is  a  constant  and  limiting  resistance  due 
to  the  battery,  conducting-  wires,  etc.,  no  matter  how  small  the 
resistance  to  be  measured  is. 

The  case  very  roughly  approximates  that  of  a  balance  whose 
sensitiveness  varies  inversely  as  the  weights  to  be  determined. 

Thomson's  Double  Bridge. — This  is  one  of  the  most  satisfactory 
and  convenient  methods  for  the  measurement  of  low  resistance. 

The  arrangement  of  the  experiment  is  shown  by  the  diagram, 
Fig.  ii. 

If  the  ratio  coils  A,  A',  are  each  made  equal  to  100  ohms,  and 
the  coils  B,  B',  each  equal  to  10  ohms,  then  when  R  :  x  ::  100  :  10 


FIG.    II. 


there  will  be  no  deflection  of  the  galvanometer  on  closing  the 
circuit. 

R  is  the  known  variable  resistance  and  x  is  the  resistance  to 
be  determined. 

The  principle  is  as  follows  :  If  there  be  no  junction  between 
R  and  x,  that  is,  if  r  =  a  ,  and  then  if  R  and  x  are  zero,  we  have 
the  ordinary  case  of  the  Wheatstone  Bridge,  100  :  10  ::  ico  :  10, 
and  the  potential  at  g,  g',  will  be  the  same. 

If  x  is  given  a  value,  and  R  is  changed  until  equal  to  10  x,  we 
have:  . 

ioo  :  10  ::  ,00  +  10  x  :  10  +  x,  or  £2?  =  I0('°  +  x)  =  £5, 

10  10  -f-  X  I 

which  is  again  the  condition  of  equal  potential  at^-and^'.  That 
is,  ioo  :  jo  ;;  R  :  x,  when  the  galvanometer  shows  no  deflection 


LOW  RESISTANCE.  21 

If  now  R  and  x  be  joined  by  any  resistance  r,  if  R  be  zero,  we 
have  : 

R  I OO  IO 

-_  =  —  =  — ,  or  ioo  :  10  ::  R  :  x. 
x          10          i 

But  zero  and  oc  are  the  limiting  values  for  small  R  ;  hence 
whatever  the  resistance  of  r,  it  does  not  effect  the  potential  at 
g,  g'.  That  is,  it  simply  shunts  off  a  portion  of  the  current, 
leaving  the  potential  at  g,  g'  still  the  same. 

The  resistance  of  the  movable  contacts  a,  a' ,  and  /£,  b't  together 
with  the  wires  leading  to  them,  is  added  to  that  of  the  ratio  coils. 
Hence  the  resistance  of  these  coils  should  be  so  great  that  the 
above  mentioned  resistance  may  be  negligible  compared  to  them. 
The  smaller  coils  ought  not  to  be  less  than  10  ohms. 


FIG.   12. 


The  contact  points  ay  a\  and  b,  b\  must  occupy  the  same  rela- 
tive positions  as  shown  in  the  diagram.  If,  for  instance,  they 
should  be  placed  in  the  positions  a,  a',  b' ,  b,  it  would  be  impos- 
sible to  obtain  a  balance. 

Again,  on  first  setting  up  the  experiment,  the  terminals  a,  a\ 
should  be  joined  to  one  point  in  the  circuit,  and  the  terminals 
b,  b\  to  some  other  point  in  the  circuit.  Then  if,  on  closing  the 
key,  there  is  any  deflection,  a  compensating  resistance  should 
be  added  to  one  of  the  coils  until  there  is  no  deflection. 

Special  coils  may  be  used  for  the  ratios,  or  a  p.  o.  bridge  and 
rheostat  can  be  employed  according  to  Fig.  12, 

A  portable  form  of  Thomson's  bridge  is  manufactured  by 
Siemens  &  Halske.  The  standard  low  resistance  is  a  thick  wire, 


22  ELECTRICAL  MEASUREMENTS. 

stretched  around  the  instrument,  and  a  movable  contact  is  ar- 
ranged so  as  to  include  more  or  less  of  the  wire.  Peg  resistances 
are  arranged  so  that  the  resistance  can  be  multiplied  or  divided, 
so  that  the  range  of  the  instrument  is  very  large. 

A  good  method  of  procedure  is  the  following  :  A  metre  of 
G.  s.  wire  of  about  o.  i  ohm  resistance  is  accurately  measured  on 
the  P.  o.  bridge,  and  its  resistance  per  mm.  calculated.  The 
wire  is  then  stretched  over  a  metre  stick,  and  used  as  the  known 
resistance  in  the  double  bridge  to  determine  the  resistance  of  a 
second  metre  of  copper  wire.  This  last  wire  is  employed  to 
measure  the  resistance  of  a  still  larger  copper  wire. 


FIG.  13. 


We  then  have  three  standard  wires  and  make  use  of  either 
one  or  the  other,  according  to  how  low  the  resistance  is  that 
must  be  determined.  The  arrangement  is  best  shown  by  the 
diagram. 

It  is  evident  that  the  measurement  is  only  limited  by  the 
sensitiveness  of  the  galvanometer  and  the  strength  of  current 
that  may  be  employed. 

A  D'Arsonval  galvanometer  or  a  Thomson  high  resistance 
galvanometer  should  be  used.  The  Thomson  low  resistance 
galvanometer  is  too  strongly  effected  by  thermal  currents, 
although  it  is  far  more  sensitive. 


LOW  RESISTANCE.  23 

Using  a  copper  wire  with  a  resistance  of  about  .000002  ohm 
per  mm.,  two  "  Samson  "  cells  in  parallel,  and  a  D'Arsonval 
galvanometer  with  a  "sensitiveness  "  of  only  about  50  micro- volts, 
it  is  possible  (if  a  telescope  and  scale  be  used  to  observe  the 
galvanometer  deflections)  to  make  measurements  to  about 
.000001  ohm. 

Now  it  is  easy  to  obtain  galvanometers  with  a  sensitiveness 
of  i  micro-volt,  and  twice  the  current  strength  may  well  be  em- 
ployed. The  measurement  could  then  be  made  to  .0000000  r 
ohm.  That  is,  a  millionth  of  an  ohm  may  be  measured  with  an 
accuracy  of  one  per  cent. 

We  may  place  the  limit  of  what  seems  at  present  the  lowest 


FIG.  14. 


possible  resistance   measurement   at  about  .ooocooooi  ohm,  or 
the  one  billionth  of  an  ohm. 

Differential  Galvanometer. — A  very  similar  method  to  the  one 
just  described  is  that  where  a  differential  galvanometer  is  em- 
ployed. In  this  case,  it  is  possible  that  even  considerably  lower 
resistances  may  be  determined  than  with  Thomson's  double 
bridge  ;  but  a  special  form  of  galvanometer  is  required. 

If  the  coils  d,  d ',  Fig.  14,  have  an  equal  and  opposite  effect  on 
the  galvanometer  needle,  then  when  the  p.  D.  between  a,  a\  equals 
that  between  b,  b' ,  there  will  be  no  deflection,  and  the  resistance 
of  R  will  equal  x. 

R  is  a  standard  wire  or  bar  with  adjustable  contacts  a,  a'.  The 
resistance  per  scale  division  is  accurately  determined  by  the 
step-down  method  given  for  the  double  bridge. 


24  ELECTRICAL  MEASUREMENTS. 

When  it  is  desired  to  have  the  ratio  of  R  to  x  as  10  :  i,  a  re- 
sistance, r,  is  added  to  the  coil,  such  that  r  +  d  —  10  d'y  then 
there  must  be  ten  times  the  p.  D.  between  a,  a',  that  there  is 
between  b,  b\  before  the  current  through  the  coil  </will  be  the 
same  as  that  through  d'. 

Hence,  when  R  is  adjusted  to  no  deflection,  R  :  x  ::  10  :  i. 

At  the  commencement  of  the  measurement,  whether  the  ad- 
ditional resistance  is  used  or  not,  the  coils  d,  d'  should  be  tested 
for  differentially.  This  is  accomplished  by  joining  the  wires  a 
and  b  to  some  point  of  the  circuit,  and  the  wires  a'-  and  b'  to  some 
other  point  of  the  circuit. 

If  there  be  a  deflection  on  closing  the  key,  a  small  auxiliary 
resistance  is  added  to  one  of  the  coils  until  there  is  no  deflec- 
tion. 

/  t1 


TT]      .  'j    x  I 

C 

bci)  U)  (P 

§ 

f 

!                         i 

L,       ' 

r 

1              i              rJ 

A           1            I     ?.i 

1    'a' 

Of 

1  3  *     '*i  * 

a, 

r 

h    ^ 

L 

LI         ^ 

FIG.  15. 

Projection  of  Potentials. — The  very  smallest  resistances  could 
easily  be  determined  by  this  method,  were  it  not  for  the  many 
practical  difficulties. 

Let  the  standard  resistance  R  and  the  unknown  resistance  x  be 
joined  in  parallel  with  the  bridge  wire  A,  B,  Fig.  15.  One  terminal 
of  the  galvanometer  is  joined  to  some  point  on  the  standard  bar, 
and  the  other  terminal  a±  is  adjusted  on  the  bridge  wire  A,  B,  to 
no  deflection.  Similar  adjustments  are  made  at  the  points  a ',  £, 
b' ;  then  A  :  B  ::  R  :  x.  A  and  B  are  the  lengths  of  the  bridge 
wire  included  between  the  points  a±  a2  and  ^  Aj.» 

The  principle  of  the  method  is  as  follows  :  Since  the  point  a, 
Fig.  1 6,  is  at  the  same  potential  as  the  point  alt  which  is  shown 
by  no  deflection  of  the  galvanometer,  and  the  point  a!  at  the  same 
dotential  as  the  point  a2,  there  must  be  the  same  p.  D.  between 


LOW  RESISTANCE.  25 

a,  a'  that  there  is  between  alt  azi  and  likewise  the  same  p.  D.  be- 
tween b,  b'  that  there  is  between  bv,  bz. 

If  these  potential  differences  are  represented  by  E,  E',  %,  E2, 
then  R  :  x  ::  E  :  E',  but  E  =  EJ  and  E'  =  E2,  hence  R  :  x  ::  EJ  :  E2, 
but  E!  :  E2  ::  A  :  B,  .  •.  A  :  B  ::  R  :  x. 

The  method  is  an  excellent  one  for  moderately  low  resistances, 
provided  that  R  be  nearly  of  the  same  value  as  x  ;  for  if  the 
ratio  be  very  unequal,  the  length  of  the  wire  A,  B,  corresponding 
to  the  smaller  resistance  will  not  be  great  enough  to  obtain  an 
accurate  reading. 

For  very  low  resistances,  the  ratio  of  the  leads  and  contacts  to 
the  resistances  to  be  determined  may  become  so  great  that  but 


OF  THK 

UNIVERSITY 


FIG.  I 6. 


a  small  portion  of  the  wire  will  remain  available  for  the  desired 
readings. 

This  difficulty  may  be  partly  overcome  by  adjusting  the  posi- 
tion of  the  battery  terminals  until  the  points,  a^  b^  fall  near  the 
ends  of  the  ratio  wire. 

Fall  of  Potential. — This  method  is  exceedingly  convenient  for 
all  ordinary  measurements  of  low  resistance. 

A  high  resistance  galvanometer  is  shunted  across  a  known  re- 
sistance, R,  Fig.  17,  and  the  deflection,  d,  is  observed.  The  deflec- 
tion d'  across  the  unknown  resistance,  x,  is  then  read,  then  d\  d'  :: 
R  :  x.  This  assumes  that  the  current  is  constant  during  the  ex- 
periment. The  resistance  of  the  galvanometer  should  be  great 


26  ELECTRICAL  MEASUREMENTS. 

compared  to  the  resistances  R  and  x.     The  readings  should  be 
taken  quickly  to  avoid  polarization  and  thermal  effects. 

If  R  be  a  standard  wire  or  bar  placed  over  a  divided  scale  and 
the  resistance  per  division  be  known,  then  R  may  be  adjusted 
until  d  =  d'  and  we  have  R  =  x. 


FIG.    17. 

A  voltmeter  may  be  employed  in  place  of  the  galvanometer 
where  the  resistances  are  not  very  low. 

If  the  galvanometer  has  a  sensitiveness  of  one  micro-volt,  and 
the  resistance  in  the  circuit  is  0.5  ohm,  then  with  a  p.  D.  of  two 
volts  a  deflection  of  one  scale  division  would  correspond  to  0.25 
micro-ohm. 


POTENTIOMETER 


FIG.   1  8. 


Potentiometer  Method.  —  This  method  is  simply  a  modification  of 
the  one  just  described. 

The  arrangement  of  the  experiment  is  indicated  by  the  dia- 
gram, Fig.  1  8.  The  potentiometer  reading  is  taken  across  R  and 


LOW  RESISTANCE.  27 

then  across  x.  The  readings  are  directly  proportional  to  the  resis- 
tances. The  galvanometer  should  give  no  deflection  when  the 
adjustment  is  correct. 

Carey  Foster's  Method- — Where  the  ordinary  Wheatstone  wire 
bridge  is  employed  for  resistance  work,  this  method  may  be 
found  convenient. 

r±  rz  are  approximately  equal  resistances,  say  one  ohm  coils. 
x  is  the  resistance  to  be  determined,  and  b  a  copper  contact 
piece,  Fig.  19.  A  balance  is  obtained  in  the  position  shown  in  the 
diagram,  x  and  b  are  then  reversed  and  the  galvanometer  slider 


again  adjusted  to  no  deflection.  The  length  of  bridge  wire  a, 
included  between  these  two  positions,  is  then  equal  in  resistance 
to  the  difference  of  resistance  between  x  and  b.  The  resistance 
of  the  bridge  wire  per  division  may  be  determined'  by  using, 
say,  o.  i  ohm  in  place  of  x. 

The  method  is  approximate  and  not  applicable  to  very  low 
resistances. 

It  assumes  that  the  contact  resistances  are  the  same  in  both 
positions  and  that  b  is  negligibly  small  compared  to  x. 


CHAPTER  IV. 
THE  WHEATSTONE  BRIDGE. 

All  ordinary  cases  of  medium  resistance  may  be  accurately 
and  conveniently  determined  by  the  Wheatstone  Bridge. 

The  demonstration  of  the  principle  of  this  method  is  similar 
to  that  given  for  the  projection  of  equi-potentials. 

Let  R  be  a  known  resistance,  x  the  resistance  to  be  measured, 
and  A  and  B  resistances  whose  ratios  are  known,  Fig.  20  ;  then, 
if  on  closing  the  circuit  there  is  no  deflection  of  the  galvano- 
meter, A  :  B  ::  R  :  x. 

Since  the  galvanometer  shows  no  flow  of  current  between  g 
and  g',  the  potential  at  these  points  must  be  the  same,  and  since 
the  other  ends  of  R  and  A  are  joined  the  potential  at  this  point 
must  be  the  same.  Consequently,  there  is  the  same  p.  D.  across 
R  that  there  is  across  A,  and  similarly  the  same  p.  D.  across  x 
that  there  is  across  B. 

But  from  Ohm's  law  R  :  x  : :  p.  D.  across  R  :  p.  D  .  across  x, 
also  A  :  B  ::  p.  D.  across  A  :  p.  D.  across  B,  and  from  the  above, 
R  :  x  ::  P.  D.  across  A  :  p.  D.  across  B,  or  R  :  x  ::  A  :  B. 

The  Wheatstone  Bridge  may  be  termed  an  electrical  balance 
in  which  the  resistances  compared  are  directly  proportional  to 
the  balance  arms. 

The  positions  of  the  battery  and  galvanometer  are  inter- 
changeable, but  the  greatest  sensitiveness  is  obtained  when  that 
which  has  the  higher  resistance  is  placed  at  the  junction  of  the 
two  higher  resistances. 

The  sensitiveness  is  also  greater  the  more  nearly  equal  are 
the  resistances  A,  B,  R,  x. 

The  Wheatstone  Bridge  is  used  in  a  great  variety  of  forms, 
but  there  are  two  general  classes  :  That  in  which  the  ratio  of 
A  to  B  is  varied  while  R  remains  the  same,  and  that  in  which  the 
ratio  of  A  to  B  is  given  a  constant  value  while  R  is  varied  until 
there  is  equilibrium. 

The  following  is  a  list  of  these  different  forms  of  bridges  : 

28 


WHEATSTONE  BRIDGE. 


29 


VARIABLE  RATIO.  . 


f  Straight  (Metre.) 
\  Circular  (Kohlrausch,  Siemens. 
<  Parallel  (Poggendorff.) 
L  Direct  Reading  (Kirchhoff.) 


(  Jjuplex  (VarJey.) 

Slide  Coil  Bridge.   \  Quadruplex  (Muirhead. 
/  Five  Arc  *  (Cushman.) 


CONSTANT  RATIO.  . 


P.  O  Bridge. 


Decade  Bridge . .  . 


(Cushman.) 

Elliot  Pattern. 
Western  El.  Pattern. 

Straight  Pattern. 
Dial  Pattern. 


In  the  ordinary  wire  bridge,  known  as  the  metre  bridge,  or 
B.  A.  bridge,  the  ratios  A,  B,  consist  of  a  G.  S.  wire,  of  which  the 


FIG.     20. 

lengths  may  be  accurately  measured  by  means  of  a  metre  scale  f 
over  which  the  galvanometer  slider  moves. 

It  is  evident  that  the  nearer  the  point  g'  is  to  the  centre  of 
A,  B,  the  less  will  be  the  effect  on  the  measurement  of  any  given 
error  in  reading  the  scale. 

The  ends  of  the  bridge  are  assumed  to  have  no  appreciable 
resistance  compared  to  the  other  resistances  in  the  circuit ;  but 
if  the  resistance  to  be  measured  is  very  low,  this  is  not  true. 
This  resistance  may  be  determined  and  corrected  for,  but  since 
the  contact  resistances  cannot  be  eliminated,  it  is  better  to  em- 
ploy one  of  the  special  methods  for  very  low  resistance  work. 

This  bridge  is  not  suitable  for  very  high  resistance  measure- 
ment, for  the  wire  A,  B,  being  of  comparatively  low  resistance, 
acts  as  a  shunt  either  to  the  battery  or  galvanometer.  The 


30  ELECTRICAL  MEASUREMENTS. 

ratio  wire  is  often  stretched  around  a  divided  circle  ;  this  renders 
the  birdge  much  more  compact. 

In  the  Siemens'  bridge,  a  circular  wire  is  used  in  combination 
with  a  set  of  standard  resistances  and  a  galvanometer. 


FIG.   21. 

The  Kohlrausch  bridge  has  the  wire  wound  on  a  drum  ;  by 
this  means  a  considerable  length  of  wire  may  be  employed  and 
very  accurate  readings  obtained. 

Another  method  of  increasing  the  length  of  the  wire  is  to 
have  it  stretched  parallel  as  in  the  Poggendorff  bridge. 

A  form  of  bridge,  where  instead  of  finding  the  ratio  of  A  to  B, 


M 


FIG.  22. 


the  resistance  is  directly  read  off,  is  known  as»the  direct  reading 
bridge  or  Kirchhoff  bridge. 

Referring  to  the  diagram,  Fig.  22,  it  is  necessary  that  the  re- 
sistances should  be  in  the  following  proportion  : 


MD:  MK::  FD:  FH. 


WHEATSTONE  BRIDGE.  31 

Suppose  these  be  given  some  definite  value  such  as  .  3  :  3  : : 
.2  :  2.  Then  when  x  =  o,  g  will  be  at  M  ;  but  if  g  is  at  K,  then 
3.3  :  x  ::  .2  :  2,  and  x  =  33.  Consequently  the  wire  M  K  should 
be  divided  into  33  parts. 

Suppose  a  bridge  reading  up  to  10  ohms  is  required,  then 


/  o  o 


FIG.  23. 


MK:  MD::  FH:  FD,  and  10:  M  K  -{-  M  D  —  FH:  FD. 

A  laboratory  form  of  this  bridge  is  shown  in  Fig.  23. 

In  the  commercial  form  of  instrument  known  ss  "  Cardew's 
lighting  conductor  bridge,"  a  circular  bridge  wire  is  employed. 

Slide  Coil  Bridges. — When  high  resistances  are  to  be  compared, 
the  ratio  resistances  A  and  B  should  also  be  high. 

In  order  to  accomplish  this,  a  series  of  coils  may  be  used  in 


FIG.  24. 

place  of  the  bridge  wire.  Suppose  we  have  ten  10  ohm  coils  in 
series,  it  would  be  equivalent  to  a  bridge  wire  of  100  ohms  re- 
sistance that  could  only  be  read  to  tenths,  Fig.  24. 

If,  instead  of  this,  eleven  10  ohm  coils  be  employed,  and  a 
second  series  of  ten  2  ohm  coils  be  arranged  so  that  they  may 


32  ELECTRICAL  MEASUREMENTS. 

be  paralleled  across  any  two  of  the  first  series,  Fig.  25,  the  entire 
resistance  will  still  be  100  ohms.  The  galvanometer  slider  may 
then  make  contact  at  any  junction  of  the  second  series,  and  by  this 
means  readings  obtained  to  y^th.  This  arrangement  constitutes 
practically  an  electrical  vernier.  The  principle  may  be  extended 

||    COILS         TEN     OHMS    EACH 

+  -•<V\P^A/AAP^^ 


10    COILS       TVVOOHMS     CACH 


L<VvKV\/>VyAA^^ 


FIG.  25. 

indefinitely  in  either  direction.  The  following  conditions  should 
be  observed :  The  entire  resistance  of  the  last  series  of  coils 
must  be  equal  to  the  resistance  of  two  coils  in  the  preceeding 
series.  If  there  be  10  coils  in  the  last  series,  the  others  must 
contain  n  coils,  or  if  100,  then  101,  etc. 

The  resistance  of  the  coils  in  the  last  series  should  not  be  so 
low  that  they  cannot  be  accurately  adjusted. 

The  principle  may  be  shown  by  referring  to  Fig.  26.  Since 
the  P.  D.  is  proportional  to  the  resistance,  the  p.  D.  from  A  to  B  is 
the  same  as  that  across  10  ohms.  Consequently  the  p.  D.  across 


FIG.  26. 

20  ohms  in  either  of  the  parallel  branches  i&  the  same  as  that 
across  10  ohms  in  the  direct  circuit.  Therefore  the  p.  D.  across 
2  ohms  in  one  of  the  parallels  is  -fa  the  p.  D.  across  10  ohrhs  in 
the  direct  circuit. 

Probably  the  best  known   form  of  slide  coil  bridge  is  the 


WHEATSTONE  BRIDGE. 


33 


Thomson -Varley  instrument.     This  employs  101  coils  of  1,000 
ohms,  and  100  coils  of  20  ohms,  Fig1.  27. 


JOOO        Ohms    E.OLCK 

FIG.    27. 


1.0      OKmt    LacK. 


The  entire  resistance  is  100,000  ohms,  and  it  gives  readings  to 
'  rhr*  or  -0001-     The  coils  are  arranged  in  two  dials. 

The  Muirhead  pattern  has  four 
series  of  coils,  3  of  IT  each  and  i 
of  i  o  coils ;  the  coils  are  arranged 
in  dials.  The  reading  is  :  -fa  X 
iV  X  •jV  X  -j1^,  or  YTJ"  ooo* 
10,000  ohm  bridge  is  employed,  the 
following  would  be  the  values  of 
the  resistances  in  the  different 
series  : 

First.     1,000  ohms  (n  coils). 

Second.    200       "  " 

Third.        40       " 

Fourth.        8       "       (10  coils). 

The  Cushman  five  arc  instru- 
ment, Fig.  28,  possesses  many  ad- 
vantages. It  employs  : 

IT  coils  of  10,000  ohms  each. 

II          "         "         2,000          "  " 

ii      "      "         400       "          " 

n      "      «  80       "          " 

10      "      "  16       "          " 

The  entire  resistance  is  100,000 
ohms,  while  readings  may  be  ob- 
tained to  ^V  X  A  X  iV  X  A  X  A*  <>r 


FIG.  28. 


By  this  means  the  range  of  the  bridge  is  increased  TO  times 


34 


ELECTRICAL  MEASUREMENTS. 


over  that  of  the  Varley  Bridge,  and  but  54  coils  are  used  instead 
of  201.  With  this  instrument,  resistances  whose  ratio  is  as  great 
as  ioco  :  i  may  be  compared  with  an  accuracy  of  about  one  per 
cent.  When  the  resistances  are  equal^  of  course,  they  may  be 
compared  to  .002  per  cent;  but  errors  due  to  temperature  co- 
efficients, contacts,  adjustment  of  the  coils,  etc.,  would  probably 
be  much  greater  than  this. 

Each  series  of  coils  is  provided  with  binding  posts,  so  that  any 
of  the  higher  series  may  be  left  out  when  a  lower  resistance 
bridge  is  desired. 

For  quick  work,  the  settings  of  the  lower  series  may  be 
omitted. 

The  arrangement  of  the  coils  in  arcs  gives  great  ease  and 
rapidity  of  adjustment. 


000  100 


100          1000 


B 


I        Z      3       «*      5 


5000  1000  1000  (000 


FIG.  29. 

The  slide  coil  bridges  described  above  are  generally  known  as 
"  potentiometers  "  on  account  of  their  employment  in  the  com- 
parison of  potential  differences. 

For  most  resistance  work,  the  constant  ratio  form  of  Wheat- 
stone  bridge  is  to  be  recommended. 

The  two  patterns  of  the  P.  O.  bridge  are  shown  in  diagrams 
29  and  30. 

A  and  B  may  be  given  several  different  values,  such  as  1000  :  10 
etc.  R  can  be  adjusted  from  one  ohm  to  10,000  ohms.  Resis- 
tances are  inserted  by,  removing  pegs. 

The  ratio  of  A  to  B  is  determined  by  the  resistance  to  be  meas- 
ured. If  x  is  very  low,  A  should  be  as  great  a's  possible  and  B  as 
small  as  possible,  thus  :  1000  :  10  :  :  R  :  x. 

For  higher  resistances  A  and  B  should  not  be  made  so  unequal 
that  a  change  of  one  unit  in  the  adjustment  of  R  will  not  be 
shown  by  the  galvanometer, 


WHEATSTONE  BRIDGE. 


35 


If  the  galvanometer  does  not  show  a  change  of  several  units 
in  R,  A  must  be  made  equal  to  B  and  as  nearly  equal  to  x  as  pos- 
sible. Thus,  suppose  x  is  about  1,000  ohms,  then  we  may  have 
1,000  :  1,000  :  :  R  :  x. 

If  x  be  very  great,  say  about  1,000,000  ohms,  then  we  must 
have  10  :  1,000  :  :  R  :  x. 

Thus  the  range  of  these  bridges  is  from  .01  ohm  to  1,000,000 
ohms,  though,  of  course,  it  may  be  increased  by  the  use  of  addi- 
tional resistance  coils  in  A  and  B  or  R. 

For  accurate  work  in  the  measurement  of  low  resistance,  such 
as  the  determination  of  specific  resistance,  special  manipulation 
is  required. 

To  the  binding  posts  1 1'  Fig.  30,  clips  are  added  and  the  ends  of 
the  bridge  are  thus  brought  near  together.  The  circuit  is  then 


FIG.  30. 

closed  by  inserting  a  wide,  thick  piece  of  copper  between  the 
clips.  The  oc  peg  is  then  removed  and  a  piece  of  fine  copper 
wire  is  joined  to  the  posts  s  s'.  The  ratio  of  A  to  B  is  made 
i, coo  :  10.  The  length  of  the  auxiliary  wire  is  then  adjusted 
until  there  is  no  deflection  on  closing  the  circuit. 

The  resistance  of  this  wire  compensates  for  the  resistance  of 
the  peg  row,  contacts,  clips  etc.  The  copper  plate  between  the 
clips  is  then  removed  and  the  resistance  to  be  measured  is  joined 
to  the  clips. 

With  a  sensitive  reflecting  galvanometer,  resistances  far  be- 
low .01  ohm  may  be  determined  by  interpolation. 

The  operation  is  as  follows  :  Suppose,  when  R  =  4  ohms,  a 
deflection  of  250  scale  divisions  to  the  left  is  obtained,  and  when 


36  ELECTRICAL  MEASUREMENTS. 

R  =  5  ohms,  a  deflection  of  150  divisions  to  the  right  is  obtained. 
Then  the  exact  value  of  R  is  4}££  ohms  =  4.625  ohms,  and 
1000  :  10  :  :  4.265  :  x,  or  x  =  .0427  ohm. 

At  the  beginning  of  the  measurement,  the  galvanometer  key 
k'  should  be  closed  ;  if  there  is  a  deflection  it  is  due  to  thermal 
currents.  The  battery  key  k  is  then  closed,  leaving  the  key  k' 
open  ;  if  there  is  a  deflection,  it  is  due  to  induction.  These 
effects  should  be  corrected  for. 

Generally,  it  is  better  to  connect  the  battery  to  the  posts  /  £, 
as  indicated  in  Fig.  30.  If  the  battery  had  a  low  internal  re- 
sistance and  were  joined  to  the  posts  /'  k',  in  the  case  where  the 
compensating  resistance  is  being  adjusted  or  where  x  is  a  very 


r-          -A-        -B- 
i 


<S^A0A<gA©vA^^ 

I  Tens  | 

I 

&A/xa/vtZXy(iw 


Hu rta r e  a. s 


(|MO^{EX4/tDvAr©vV^^ 

o 


FIG.  31. 

low  resistance,  it  would  practically  be  short  circuited.  More- 
over, the  heavy  current  thus  obtained  would  heat  the  resis- 
tances and  tend  to  destroy  the  balance. 

The  Decade  pattern  of  Wheatstone  Bridge  involves  the  same 
principles  of  construction  as  those  just  described.  But  the  ar- 
rangement of  the  coils  is  somewhat  different. 

This  arrangement  is  shown  for  a  portion  of  R  in  diagrams  3 1 
and  32.  There  are  10  one  ohm  coils  in  series*,  10  ten  ohm  coils, 
etc.;  these  coils  may  be  placed  in  parallel  rows  or  arranged 
circularly  as  in  the  dial  pattern. 

Each  terminal  marked  zero  is  connected  to  the  next  preced- 
ing contact  bar  or  circular  contact  block. 


WHEATSTONE  BRIDGE. 


37 


The  number  of  coils  thrown  in  circuit  in  any  row  or  circle  de- 
pends on  the  position  of  the  peg  in  that  particular  row  or  circle. 

In  the  dial  form,  a  rotating  contact  piece  may  be  used  in  place 
of  a  peg.  The  reading  of  R  in  the  diagram  given  would  be  462. 

The  advantage  of  this  form  of  bridge  is  that  the  value  of  R 
may  be  read  off  directly,  while  in  the  p.  o.  bridge  the  resistances 
must  be  added  up.  There  are  also  fewer  pegs  to  manipulate, 
and  where  sliding  contact  pieces  are  employed  the  adjustment 


can  be  made  with  much  more  rapidity.  The  number  of  coils 
required  in  this  style  of  instrument  is,  however,  considerably 
greater  than  in  the  p.  o  bridge. 

In  a  form  of  the  Decade  set  known  as  the  Anthony  Bridge 
the  resistance  coils  may  be  connected  in  parallel  as  well  as  in 
series.  The  lowest  coils  in  R  being  one  tenth  ohm,  when  multi- 
pled  give  Tfg-  ohm,  and  since  the  ratio  of  A  to  B  may  be  made 
10,000  :  i,  the  range  of  this  bridge  is  theoretically  from  i  X  io~* 
ohm  to  100  meg-ohms. 


CHAPTER   V. 


SPECIFIC  RESISTANCE  AND  GALVANOMETER  RESISTANCE. 


Specific  Resistance  is  the  ratio  of  the  resistance  of  any  material 
to  the  resistance  of  any  given  material  of  the  same  dimensions 
under  the  same  conditions  taken  as  a  standard. 

The  standard  adopted  is  pure  copper,  and  tables  are  made  out 
giving  the  resistances  of  various  lengths  of  copper  wire  of  dif- 
ferent diameters  at  several  temperatures. 

The  best  table  is  probably  that  adopted  by  the  American  In- 
stitute of  Electrical  Engineers.  The  data  from  which  this  table 
has  been  computed  are  as  follows  : 

Matthiessen's  standard  one  metre-gramme  hard  drawn  copper 

=  0.1469  B.  A.  ohms  @  OQ  C. 
"  "  "  "     soft  drawn  copper  =  0.1437 

B.  A.  ohms  @  o°  C. 

"  "  "  "     soft  drawn  copper  =  0.1417 

international  ohms  @  oy  C. 
Sp.  Gr.  of  copper  =  8.89. 

Temp.  coef.  for  20°  C  =  1.0797.     [.21  per  cent,  per  degree  F.] 
One  B.  A.  ohm  =  0.9866  international  ohms. 
One  Legal  ohm  =  0.9972 

The  table  is  made  out  in  international  ohms.  One  column 
gives  the  ohms  per  foot  @  20°  C.  of  wire  of  various  diameters. 
Thus,  No.  20  wire,  diameter  =  0.03196  inch,  resistance  =  0.01014 
ohm  @  20°  C. 

Since  the  resistance  varies  directly  as  the  length  and  inversely 
as  the  square  of  the  diameter.  A  single  constant  like  the  above 
might  be  used  for  the  calculation  of  specific  resistance. 

The  determination  of  specific  resistance  may  be  made  as  fol- 
lows :  A  convenient  length  of  the  wire  is  taken  and  its  resis- 
tance accurately  measured  on  the  p.  o.  bridge  according  to  the 
directions  given.  The  resistance  thus  found!  is  divided  by  the 
length  and  the  resistance  per  foot  obtained.  The  diameter  of 
the  wire  is  then  determined  with  micrometer  calipers  or  wire 
gauge. 

The  resistance  per  foot  is  divided  by  the  resistance  per  foot 

38 


SPECIFIC  RESISTANCE.  39 

of  copper  wire  of  the  same  diameter,  @  20°  C.,  the  value  being 
taken  from  the  table. 

For  copper,  the  reciprocal  of  the  above  is  taken  and  the  re- 
sult expressed  in  per  cent,  of  conductivity.  If  the  bridge  em- 
ployed is  in  B.  A.  ohms  or  legal  ohms,  the  resistance  should  be 
reduced  to  international  ohms. 

If  the  temperature  is  much  different  from  20°  C.,  a  correction 
should  be  made. 

In  general,  the  resistance  of  alloys  is  much  higher  than  that 
of  any  of  their  constituents,  while  the  temperature  coefficient  is 
lower  and  may  even  be  negative. 

The  Conductivity  Balance  is  practically  a  Wheatstone  Bridge, 
in  which  R  consists  of  a  standard  copper  wire  of  given  length 


<S 


1 


FIG.  33. 

and  weight.  The  length  of  the  sample  of  wire  to  be  determined 
is  then  varied  until  a  balance  is  obtained,  and  from  its  length 
and  weight  the  specific  resistance  is  calculated. 

It  is  scarcely  less  trouble  than  the  ordinary  method,  and  since 
the  resistance  of  the  standard  may  change,  it  is  doubtful  if  re- 
sults obtained  can  always  be  relied  upon. 

Galvanometer  Resistance. — The  resistance  of  a  galvanometer 
may  be  measured  by  the  p.  o.  bridge  in  the  usual  manner,  but 
if  it  be  a  Thomson  galvanometer,  the  coils  should  be  turned 
until  the  needles  are  in  the  axis  of  the  coils  ;  the  galvanometer, 
whose  resistance  is  being  measured,  should  be  placed  at  such  a 
distance  from  the  other  galvanometer,  or  in  such  a  position  with 
reference  to  it,  that  there  will  be  no  deflection  produced  by 
inductive  action  of  its  coils. 


40  ELECTRICAL  MEASUREMENTS. 

When  only  one  galvanometer  is  available,  Thomson's  method 
can  be  employed.  The  galvanometer  is  put  in  place  of  the  un- 
known resistance  in  the  P.  o.  bridge,  Fig.  33,  the  ends  of  the 
bridge  being  joined  by  a  wire  furnished  with  a  key. 

The  battery  is  joined  between  A  and  B,  and  R  and  the  galvano- 
meter. The  ratio  of  A  to  B  is  determined  by  the  galvanometer 
resistance. 

The  battery  key  is  closed,  and  the  galvanometer  deflection  is 
reduced  to  some  convenient  amount  by  lowering  the  magnet  if 
it  be  a  Thomson  galvanometer,  or  adding  an  auxiliary  resistance 
to  the  battery  circuit.  R  is  then  adjusted  until  closing  the  key 
joining  the  ends  of  the  bridge  produces  no  change  in  the  steady 
deflection. 

Then,  A  :  B  :  :  R  :  galvanometer  resistance. 

One-half  Deflection  Method. — Another  method  is  to  join  up  the 
galvanometer  in  series  with  a  rheostat  and  low  resistance  bat- 
tery. 

The  resistance  is  adjusted  until  a  convenient  deflection  is 
obtained.  Call  this  resistance  r.  The  resistance  is  then  in- 
creased until  the  deflection  is  reduced  to  one-half.  Call  this 
latter  resistance  R.  Then  if  the  deflections  are  proportional  to 
the  current,  the  resistance  in  the  second  case  must  be  twice 
that  in  the  first  case,  since  the  current  has  been  diminished  to 
one-half.  Hence : 

2  (g  +  r)  =  S  +  R>  or  S  =  R  —  2  r- 

If  the  battery  resistance  is  appreciable  compared  to  the  gal- 
vanometer resistance,  a  correction  should  be  made. 

A  modification  of  this  method  would  be  to  shunt  the  battery 
until  the  desired  deflection  is  obtained,  and  then  add  a  resistance 
R,  such  that  the  deflection  is  one-half.  Then,  g  =  R. 


CHAPTER   VI. 


j  Comparison  of  Standards. 

\  Calibration  of  Bridge  Wire  and  Rheostat. 

In  the  comparison  of  standard  ohms,  an  accuracy  of  from  .01 
per  cent,  to  .coi  per  cent,  is  desirable.  This  means  that  the  de- 
termination must  be  made  to  within  at  least  .cooi  ohm.  Some 
special  method  must,  therefore,  be  employed.  The  best  is 
Carey  Foster's  Method. 

In  the  diagram,  Fig.  34,  A,  B,  is  a  large  German  silver  wire  whose 
resistance  per  metre  has  been  accurately  measured,  and  from 
this  the  resistance  per  mm.  calculated  before  placing  the  wire  in 
position  on  the  bridge.  R,  R',  should  be  approximately  one  ohm 
each.  They  are  known  as  the  ratio  coils,  s,  s',  are  the  stand- 
ard ohms  to  be  compared.  They  are  placed  in  water  baths,  and 
contact  is  made  with  the  bridge  by  means  of  mercury  cups. 

The  galvanometer  slider  is  adjusted  on  the  wire  A,  B,  until 
there  is  no  deflection. 

The  positions  of  s,  s',  are  then  reversed  and  a  balance  again 
obtained.  The  length  of  wire,  r,  included  between  the  two  po- 
sitions of  the  galvanometer  slider  is  equal  to  the  difference  in 
resistance  between  s,  and  s'.  The  slider  is  moved  toward  the 
greater  resistance.  Example  :  Resistance  of  A,  B,  per  mm.  = 
.00005  ohm,  r  =  3  mm.,  slider  moved  toward  s'.  Then  s'  is 
greater  than  s  by  .00015  ohm  or  .015  per  cent. 

The  standards  should  be  placed  in  the  water  baths  a  consid- 
erable time  before  commencing  the  measurement,  and  the  tem- 
perature during  the  determination  carefully  noted.  Several 
observations  should  be  taken,  and  after  some  time  another  set 
obtained.  If  these  last  differ  materially  from  the  first,  it  is 
probably  due  to  the  standards  not  having  arrived  at  a  constant 
temperature. 

The  temperature  coefficient  of  the  wire  composing  standard 
ohms  may  betaken  at  about  .02  per  cent,  to  .04  per  cent,  per 
degree  C.,  so  that  a  difference  of  ^°  C.  would  have  accounted 
for  the  difference  of  resistance  in  the  above  example. 

At  the  beginning  of  the  measurement  the  galvanometer  key 

41 


42  ELECTRICAL  MEASUREMENTS. 

should  be  closed,  the  battery  key  remaining  open.  If  there  be 
a  deflection  caused  by  thermal  currents,  it  is  p'robably  due  to  the 
ends  of  the  bridge  being  at  different  temperatures. 

It  is,  therefore,  well  to  cover  the  bridge  ends  with  cotton  or 
some  other  non-conducting  material,  if  the  apparatus  is  not 
used  in  a  room  of  constant  temperature. 

It  should  also  be  noted  if  there  is  any  effect  due  to  induction. 
This  is  observed  by  closing  the  battery  key,  leaving  the  galvan- 
ometer key  open. 

Where  great  accuracy  is  required,  the  utmost  care  must  be 
exercised  throughout  the  determination. 

A  special  form  of  bridge,  such  as  the  Jenkin's  bridge,  is  usu- 
ally employed.  The  instrument  is  extremely  compact.  A  short 
standard  wire  is  used,  and  copper  blocks  with  mercury  cups  and 
commutator  so  arranged  that  the  standard  ohms  to  be  compared 


-£ 


n\  a  IOOOI.K  10  o   OIK  O_L 

3  Ol  S    IO 

•A.  i      .     i     iliii.it  —  i  1  —  _i  — 

iS       i      i        i   B 

FIG.    34. 

may  be  placed  very  near  together  and  their  positions  reversed 
by  means  of  the  commutator.  The  ratio  resistances  are  wound 
on  the  same  bobbin  and  thus  identity  of  temperature  is  in- 
sured. 

Another  method  by  which  resistances  may  be  compared  with 
considerable  accuracy  is  by  "  substitution  in  the  bridge."  In  Fig. 
35,  A,  B,  is  a  German  silver  wire,  preferably  of  about  three  or  four 
ohms  resistance.  R  is  an  auxiliary  rheostat,  i,  an  interpolation 
resistance  that  may  be  made  .001,  .01  or  .1  ohm,  and  s,  s\  the 
resistances  to  be  compared.  At  the  commencement  of  the  de- 
termination, s  and  i  are  short-circuited,  the  one  ohm  peg  is  re- 
moved in  the  rheostat,  R,  and  a  balance  against  the  standard 
resistance,  s',  is  obtained  by  moving  the  galvanometer  slider,  g', 
until  there  is  no  deflection. 

An  interpolation  resistance  of,  say  .001  ohm  is  then  added  and 


COMPARISON  OF  STANDARDS. 


43 


the  galvanometer  deflection  observed.  This  resistance  is  then 
short-circuited  and  another  observation  made  to  see  if  the  bal- 
ance remains  unchanged.  For  interpolation,  it  is  convenient  to 


I 

7T71 

Ol  R    10  C 

I    IO     O     Ol  8     IO  O  Ol   S    £ 

a= 

^  O    -    ^^ 

f   ^ 

L  I  y  _.  *7k  j  i 

FIG.    35. 

have  an  interpolation  box,  and  add  the  resistances  by  removing1 
pegs. 

If  the  balance  is  still  perfect,  s'  is  shunted  by  the  short-circuit 
piece  c',  and  the  resistance,  s,  to  be  compared  is  shown  in  cir- 
cuit. The  galvanometer  deflection  is  then  read  and  the  differ- 
ence in  resistance  calculated. 

Example  :  Interpolation  resistance  =  .001  ohm  ;  deflection  = 
1 60  (to  the  right)  ;  deflection  when  s  is  substituted  for  s'  =  40 
(to  the  left)  ;  then  s  is  less  than  s'  by  Ty^  of  .001  ohm  or  .00025 
ohm. 

The  same  precautions  with  regard  to  thermal  currents,  etc., 
should  be  taken  as  in  the  first  method. 

For  the  comparison  of  standard  ohms  the  Carey  Foster  me- 
thod should  be  employed  ;  but  where  the  resistances  in  a  rheo- 
stat are  to  be  checked  against  a  standard  resistance,  the  method 
just  described  is  particularly  applicable. 

Calibration  of  a  Bridge  Wire. — The  most  direct  and  convenient 
manner  of  checking  a  bridge 
wire  is  to  determine  the 
lengths  of  wire  that  corres- 
pond to  the  ratio  of  known 
resistances. 

Suppose  R,  R',  Fig.  36,  to  be 
two  rheostats  each  adjustable 
from  1,000  to  10,000  ohms. 
If  it  be  desired  to  step  off  the 
bridge  wire  A,  B,  into  10  parts 
of  equal  resistance,  R  is  first  FIG.  36, 


44 


ELECTRICAL  MEASUREMENTS. 


made  i,oco  ohms  and  R'  9,000  ohms,  and  g'  adjusted  to  no  de- 
flection. This  point  gives  the  first  tenth.  R  is  then  made  2,000 
and  R'  8,000,  and  the  second  point  on  the  bridge  wire  deter- 
mined, and  so  on  for  the  other  points. 

Of  course,  lower  resistances  for  R,  R',  might  be  used  if  the 
leads  were  negligibly  small  compared  to  them. 

The  resistances,  R,  R',  are  supposed  to  be  as  correct  as  the 
percentage  of  accuracy  required  in  checking  the  bridge  wire. 

It  is  important  that  the  battery  leads  be  connected  directly  to 
the  ends  of  the  bridge  wire  A,  B.  In  that  case  the  resistance  of 
the  leads  from  the  rheostats  is  added  to  the  large  resistances 
R,  R',  and  tends  but  slightly  to  disturb  their  ratio. 

In  place  of  the  two  rheostats  it  is  exceedingly  convenient  to 
employ  a  slide  coil  bridge  (or  potentiometer.)  In  Carey 
Foster's  method,  an  auxiliary  bridge  wire  A',  B',  Fig.  37,  is  made 


FIG.  37. 

use  of.  G  is  the  "  gauge  "  or  a  resistance  equal  to  the  resistance 
of  certain  length  of  A,  B,  according  to  the  desired  interval  of 
calibration,  c  is  a  copper  connecting  piece. 

The  operation  is  as  follows  :  The  "gauge  "  being  in  the  posi- 
tion shown  in  the  diagram,  g'  is  placed  very  near  the  end  of  the 
bridge  wire  at  B,  and  the  other  slider,  g,  of  the  galvanometer,  is 
adjusted  on  the  auxiliary  wire  A',  B',  to  no  deflection. 

The  positions  of  G  and  c  are  then  reversed  and  the  slider  g' 
adjusted  to  no  deflection.  G  and  c  are  replaced  in  their  former 
positions,  the  slider  g  adjusted  to  no  deflection,  and  so  on. 

By  this  means  the  bridge  wire  A,  B,  is  stepped  off  in  portions 
of  equal  resistance. 

The  resistance  of  the  "  gauge "  determines,  of  course,  the 
amount  of  displacement  of  g'  at  each  reversal.  With  the  double 
bridge,  the  wire  may  be  calibrated  by  simply  measuring  any 
convenient  resistance  on  different  portions  of  the  wire. 


CALIBRATION  OF  BRIDGE  WIRES.  45 

When  the  differential  galvanometer  is  made  use  of,  the  bridge 
wire  may  be  checked  by  determining  some  suitable  resistance  at 
different  points  along  the  wire. 

Calibration  of  a  Rheostat. — A  rheostat  may  be  calibrated  by  the 
method  of  "  Substitution  in  the  Bridge,"  previously  described. 

The  one  ohm  coil  in  the  rheostat  is  compared  to  a  standard 
ohm. 

Then  the  one  ohm  -{-  the  standard  is  balanced  against  two 
ohms  in  the  auxiliary  rheostat.  An  interpolation  resistance  is 
added  and  the  deflection  noted.  This  is  then  short-circuited 
and  the  two  ohm  coil  in  the  rheostat  to  be  calibrated  substituted 
for  the  one  coil  plus  the  standard,  the  deflection  noted  and  from 
this  the  difference  in  resistance  calculated. 

The  one  ohm  coil  -|-  the  two  ohm  coil  is  next  balanced  against 
three  ohms  in  the  auxiliary  rheostat,  interpolation  made,  and 
the  three  ohm  coil  is  then  substituted  for  the  two  ohm  coil  + 
the  one  ohm  coil,  and  the  difference  in  resistance  determined. 
By  this  means  all  of  higher  resistances  in  the  rheostat  may  be 
compared  with  the  sum  of  the  next  lower  ones. 

When  the  resistance  in  the  circuit  is  increased,  the  deflection 
of  the  galvanometer  for  any  given  change  of  resistance  grow 
less,  so  that  it  is  necessary  to  interpolate  after  each  change  of 
resistance.  It  is  better  to  have  several  resistances  for  interpo- 
lation, such  as  o.i,  o.oi  and  o.oor  ohm.  and  when  the  deflections 
become  small  to  use  one  of  the  higher  resistances. 

Since  this  is  a  deflection  method,  thermal  and  inductive  effects 
should  be  carefully  corrected  for. 


CHAPTER  VII. 
HIGH  RESISTANCE. 


f  Slide  Coil  Bridge. 
\  Fall  of  Potential.* 
I  Deflection  Method. 
[  Loss  of  Charge. 

It  is  difficult  to  define  any  exact  limit  for  the  term  "  High 
Resistance."  In  a  general  way,  any  resistance  above  100,000 
ohms  may  be  called  a  high  resistance,  though  usually  in  insula- 
tion measurements  the  unit  taken  is  a  million  ohms  or  a  meg- 
ohm (//).  Again,  in  certain  cases  of  insulation  such  as  that  of  a 
telegraph  line,  the  insulation  may  be  considerably  less  than  a 
meg-ohm.  The  term  "  insulation  "  is  applied  to  the  resistance 
of  dielectrics  and  materials  that  are  not  good  conductors. 
Thus  any  "insulation  "  is  usually  a  *•  high  resistance,"  but  any 
"  high  resistance  "  is  not  necessarily  that  of  a  dielectric  or  an 
"  insulation." 

Just  how  great  a  resistance  can  be  measured  with  the  present 
methods  it  is  hard  to  say,  but  theoretically  by  the  deflection 
method,  using  200  volts  and  a  Thomson  galvanometer  whose 
figure  of  merit  is  100,000  J2,  resistances  up  to  20,000,000  ti  might 
be  determined.  The  imperfect  insulation  of  the  apparatus, 
however,  is  likely  to  produce  considerable  error  before  reaching 
resistances  nearly  so  great  as  the  above  figure. 

The  accuracy  required  in  high  resistance  measurement  is 
much  less  than  for  the  lower  resistance  measurements,  but  in 
many  cases  of  insulation  the  resistance  of  the  dielectrics  vary 
greatly  according  to  circumstances,  and  it  is  therefore  necessary 
to  know  the  conditions  of  the  experiment  with  great  exact- 
ness. 

Slide  Coil  Bridge  Method. — Very  great  resistances  could  be 
measured  on  the  Wheatstone  Bridge  if  the  other  three  arms 
could  be  made  of  such  resistance  that  they  would  be  somewhat 
near  the  magnitude  of  that  to  be  determined.  This  require- 

*"  Fall  of  Potential"  should  be  substituted  in  place  of  '  Poientiometer "  in  the  general  classifi- 
cation. 

46 


HIGH  RESISTANCE. 


47 


ment  is  fulfilled  if  the  stand- 
ard resistance  be  at  least 
ico,ooo  ohms,  and  a  slide  coil 
bridge  of  say  100,000  ohms  be 
used  for  the  adjustable  ratio. 

The  connections  are  shown 
in  Fig.  38.  A  rather  high 
voltage  should  be  used. 

By  this  method  resistances 
of  several  meg-ohms  may  be 
determined  with  great  accu- 
racy. 


FIG.    39. 


38. 


Fall  of  Potential— Another 
method  is  to  join  the  known 
resistance  in  series  with  the 
battery  and  the  resistance  to 
be  measured.  The  E.  M.  F.  of 
the  testing  battery  E  having 
previously  been  determined 
with  a  voltmeter  or  by  other 
suitable  means,  the  p.  D.  across 
R  (E')  is  measured.  This  is 
best  accomplished  by  charg- 
ing a  condenser  across  R,  and 


discharging  it  through  a  high  resistancegalvanometer.  The  value 
of  the  deflection  so  obtained  may  be  found  by  afterwards  charg- 
ing the  condenser  with  a  standard  cell  and  noting  the  deflection. 

The  resistance  of  x  is  found  by  the  proportion  : 
E  :  E'  :  :  (R  -f-  x)  :  x* 

The  P.  D.  across  R  can  also  be  measured  with  an  electrometer 
or  a  potentiometer  and  standard  cell  may  be  used  ;  in  the  latter 
case  the  conditions  of  the  circuit  are  rather  uncertain,  and  it  is 
doubtful  if  the  results  obtained  can  be  relied  upon. 

Deflection  Method. — The  standard  method  for  nearly  all  insu- 
lation determinations  is  that  of."  direct  deflection."  Very  great 
resistances  can  be  measured  by  it,  the  conditions  of  experiment 
are  completely  under  control  and  may  be  varied  according  to 
circumstances. 

A  high  resistance  Thomson  galvanometer  is  joined  up  in  ser- 
ies with  a  known  resistance  and  testing  battery.  The  deflection 
is  then  read,  the  galvanometer  being  shunted,  and  fr6m  this  the 
"  constant  "  is  calculated. 

By  the  "  constant  "  of  the  galvanometer  is  meant  the  resis- 
tance that  must  be  introduced  into  the  circuit  to  reduce  the 
deflection  to  one  scale  division  with  any  given  battery. 


ELECTRICAL  MEASUREMENTS. 


K 


O      O 


FIG.    40. 


It  will  be  seen  that  it  de- 
pends upon  the  "  Figure  of 
merit "  of  the  galvanometer 
and  the  E.  M.  F.  used ;  but 
since  the  same  E.  M.  F.  is  em- 
ployed throughout  the  meas- 
urements, it  is  not  brought 
into  the  calculation.  After  the 
"  constant  "  is  obtained,  the 
resistance  to  be  measured  is 
substituted  in  place  of  the 
known  resistance  and  the  de- 
flection again  read.  This  de- 
flection, multiplied  by  the 
shunt,  if  one  be  used,  and 
divided  into  the  "constant," 
gives  the  resistance  desired. 
The  connections  are  indicated  by  Fig.  40.  Here  a  Kempe's 
reversing  key  is  shown. 

Example  :  R  =  100,000  ohms  (o.i  j?),  deflection  with  R  in  cir- 
cuit =  250  divisions,  when  y^Vfr  shunt  is  used  ;  then  "  constant  " 
=  o.i  J2  X  250  X  1,000  =  25,000  Q  ;  deflection  with  x  in  circuit 
=  50  divisions,  shunt  =  -f$.  Then  resistance  of  x  =  25,000  Q 
-^  50  X  10  =  50  J2. 

If  the  insulations  to  be  measured  are  not  very  great,  the 
Thomson  galvanometer  may  be  replaced  by  some  form  of 
D'Arsonval  galvanometer. 

Loss  of  Charge  Method. — For  very  high  insulations  that  cannot 
be  conveniently  measured  by  "  direct  deflection,"  this  method 
may  be  employed.  It  is  especially  useful  in  testing  joints  of 
insulated  wires.  The  connections  for  this  determination  are 
shown  in  Fig.  42. 

A  condenser  is  charged  and  the  discharge  deflection,  v,  noted. 
The  condenser  is  again  charged  using  the  same  E.  M.  F.  and  insu- 
lated for  T  seconds  with  the  resistancedto  be  measured  between 
the  poles  ;  it  is  then  discharged  and  the  deflection,  v,  noted. 

Then  if  F  =  capacity  of  condenser  in  micro-farads,  R  =  re- 
sistance in  meg-ohms  between  poles  of  condenser. 

T  • 

n    £ 

~  2.303  F  (log  V—  log  v.} 

The  resistance  of  the  condenser  should  first  be  determined 
before  placing  the  resistance  to  be  measured  between  the  poles. 
The  final  result  is,  of  course,  the  combination  of  the  two  resis- 
tances when  placed  in  multiple. 


CHAPTER  VIII. 


f  Insulating  Material — "  Specific  Insulation." 
f  Short  Lengths. 

Cable    j  Single  Core. 
,.res  J  (     >le'-j  Multiple  Core. 


INSULATION.  4   Insulated   Wires. 

(  Loss  of  charge* 
I  Joint  Testing,  -j  Accumulation. 
[  (  Electrometer. 

A  erial   Wires 

The  requirements  in  the  measurement  of  insulation  are  so 
varied  that  it  seems  best  to  make  out  a  classification  of  the  dif- 
ferent cases  and  then  treat  each  separately. 

The  resistance  of  dielectrics  differs  so  greatly  according  to 
circumstances  that  a  determination  is  of  little  value  unless  all 
of  the  conditions  are  given. 

The  E.  M.  F.  used  is  of  great  importance  ;  it  should  usually  be 
from  ioo  to  200  volts. 

It  is  true  that  if  the  insulation  is  perfect  it  is  independent  of 
the  E.  M.  F.,  but  in  a  faulty  insulation  a  high  E.  M  F.  may  dis- 
cover faults  that  a  low  one  will  not,  hence  a  determination  made 
with  a  low  E.  M.  F.  may  be  valueless. 

The  battery  should  be  very  constant,  for  if  there  is  any  ca- 
pacity in  the  circuit,  slight  variations  of  E.  M.  F.  may  produce 
considerable  variations  in  the  galvanometer  deflections. 

Secondary  batteries  are  the  best.  The  silver  chloride  testing 
cells  require  careful  handling  to  keep  in  good  order  and  may 
get  to  have  a  very  high  internal  resistance. 

Insulation  resistance  decreases  with  an  increase  of  tempera- 
ture, and  there  is  also  a  time  lag.  Hence,  it  should  be  kept  at 
the  same  temperature  for  some  time.  The  standard  tempera- 
ture is  75°  F. 

The  resistance  of  dielectrics  appears  to  increase  by  the  con- 
tinued action  of  the  current.  This  action  is  known  as  "  electri- 
fication." It  seems  to  be  due  to  a  sort  of  dielectric  polarization. 

The  deflection  should,  therefore,  be  read  after  some  stated 
time — usually  after  one  minute  "  electrification." 

49 


50  ELECTRICAL  MEASUREMENTS. 

It  is  much  more  marked  at  low  than  at  high  temperatures. 
It  depends  on  the  kind  of  material,  being  quicker  in  some  kinds 
of  gutta-percha  than  in  others,  and  is  smallest  in  the  best  qual- 
ity. 

In  the  case  of  gutta-percha  the  rate  of  fall  between  the  first 
and  second  minute  would  average  about  2  per  cent,   to  5  per 
cent.     In  india  rubber  it  may  be  as  much  as  50  per  cent,  be 
tween  the  first  and  fifth  minute. 

If  the  insulation  is  sound,  the  "  electrification  "  should  be  reg- 
ular. An  unsteady  "electrification"  is  usually 'a  sign  of  de- 
fective insulation.  It  may  be  caused,  however,  by  a  bad  con- 
dition or  insulation  of  the  battery,  imperfect  insulation  of  the 
ends  of  leads  or  cable,  or  it  may  be  due  to  currents  induced  in 
cables  when  they  are  coiled. 

There  also  seems  to  be  a  difference  of  effect  in  cable  testing, 
whether  the  +  or  —  pole  of  the  battery  is  put  to  the  cable. 
When  the  battery  is  not  reversed,  the  —  pole  should  be  joined 
to  the  cable.  The  4-  pole  seems  to  have  the  effect  of  sealing 
up  a  fault.  When  the  current  is  reversed,  a  good  insulation 
should  give  equal  deflections. 

Specific  Insulation. — This  should  be  determined  by  the  deflec- 
tion method,  substituting  the  insulating  material  in  place  of  R 
in  Fig.  40.  The  insulation  of  the  apparatus  and  leads  should 
first  be  carefully  tested.  It  is  best  to  use  a  rather  large  surface 
of  the  insulating  material.  The  contact  may  be  made  in  the 
following  manner  :  On  a  well  insulated  support  or  table  is 
placed  the  wire  leading  from  the  galvanometer  ;  next  comes  a 
piece  of  tinfoil  the  size  of  the  area  to  be  measured  ;  then  a  piece 
of  wet  felt  or  wet  blotting  paper  of  the  same  size,  and  upon  this 
the  insulite.  The  contact  above  is  made  in  the  same  way  with 
the  addition  of  a  cover  upon  which  is  placed  a  heavy  weight. 
By  this  means  good  contact  is  secured  over  the  surface  to  be 
measured. 

The  deflection  should  be  taken  after  one  minute  "  electrifica- 
tion." This  gives  the  "  absolute  "  insulation.  The  "specific 
insulation  "  is  the  insulation  of  unit  volume.  It  is  obtained 
from  the  absolute  insulation  by  multiplying  by  the  area  of  the 
contacts  and  dividing  by  the  thickness  of  the  insulating  material. 

Thus  :  Sp.  Ins.  =  Ab.  Ins.  x       area 


thickness 
The  E.  M.  F.  used  should  be  stated  and  the  temperature  at  time 

of  experiment. 

Short  Lengths  of  insulated  Wire  — When  short  lengths  of  cable, 

such  as  y±  mile  to  one  or  two  miles  are  to  be  tested  during  man- 


INSULATION.  51 

ufacture  to  obtain  the  insulation  per  mile,  the  following  method 
should  be  employed. 

The  connections  are  shown  in  the  diagram,  Fig.  41. 

The  cable  is  coiled  and  placed  in  a  tank  of  water.  One  end 
is  carefully  insulated  while  the  other  end  is  joined  to  the  circuit. 
Contact  with  the  inner  surface  of  the  insulation  is  thus  obtained 
by  means  of  the  conducting  wire,  while  contact  with  the  outer 
surface  is  secured  through  the  water  into  which  attached  to  a 
metal  plate  dips  the  wire  from  the  other  end  of  the  circuit. 
Fig.  41  is  a  general  diagram  for  cable  testing  and  does  not  show 
this  special  arrangement. 


Q- 


c\        © 

O 


J 

1 


FIG.   41.  "'-. 

The  galvanometer  is  provided  with  a  commutator,  c,  and  a 
short  circuit  key,  g,  the  battery  is  joined  to  a  key  of  'the 
Rymer-Jones  pattern.  The  cable  is  shown  in  position  for  test- 
ing. The  manipulation  is  as  follows  :  The  battery  key  being 
closed,  the  short-circuit  key,  g,  is  opened  and  the  deflections 
read  at  the  end  of  one  minute  and  two  minutes  ;  g  is  then  closed, 
the  current  reversed,  the  galvanometer  commutated  and  the  de- 
flections again  read. 

The  idea  in  commutating  the  galvanometer  is  to  obtain  the 
deflections  on  the  same  side  of  the  scale.  This  is  important 
when  the  deflections  with  first  the  —  and  then  -j-  poles  of  the 
battery  joined  to  the  cable  are  compared.  Of  course,  the  "  con- 


52  ELECTRICAL  MEASUREMENTS. 

stant "  should  also  have  been  obtained  from  deflections  on  the 
same  side  of  the  scale. 

The  short-circuit  key  must  always  be  used  in  cable  testing, 
for  cables  act  like  condensers,  having  a  capacity  of  aboul  y$  mf. 
per  mile,  and  are  charged  and  discharged  every  time  the  battery 
key  is  opened  or  closed.  This  charge  and  discharge  would,  of 
course,  take  place  through  the  galvanometer  were  it  not  shori- 
circuited. 

In  the  report,  the  insulation  after  one  minutes'  "  electrifica- 
tion "  with  the  —  pole  joined  to  the  cable  should  be  given.  The 
percentage  of  "  electrification  "  between  the  first  and  second 
minute  should  also  be  reported. 

It  is  better  to  keep  the  cable  in  the  water  for  at  least  24  hours 
before  making  the  determination.  The  standard  temperature 
for  the  water  is  75°  F.;  at  any  rate,  the  temperature  should  be 
specified. 

The  E.  M.  F.  used  should  be  stated. 

The  "  absolute  "  insulation  divided  by  the  length  expressed 
in  miles  will  give  the  insulation  per  mile. 

A  good  cable  should  have  an  insulation  of  from  about  400  Q 
to  1,000  Q  per  mile. 

Cable  Testing. — This  is  the  case  where  the  cable  is  in  position, 
either  sub-marine  or  underground.  The  connections  are  the 
same  as  Fig.  41.  The  terminal,  E,  is  "  grounded,"  and  one  end 
of  the  cable  is  insulated.  The  resistance  after  one  minutes' 
"  electrification,"  the  —  pole  being  joined  to  the  cable,  is  re- 
ported and  also  the  "electrification"  between  the  ist  and  i5th 
minutes. 

In  making  careful  tests  on  long  cables,  a  rather  complicated 
set  of  observations  is  required,  and  a  report  based  upon  these  is 
made  out. 

In  cases  of  this  kind  it  is  advisable  to  consult  "  Kempe's 
Handbook  of  Electrical  Testing." 

When  submerged  cables  are  tested,  the  "earth  current"  may 
render  the  readings  unsteady.  There  is  no  method  of  elimina- 
ting these  effects  in  single  cored  cables,  but  if  the  cable  is  mul- 
tiple cored,  a  second  core  may  be  joined  to  the  battery  in  place 
of  '*  grounding  "  it  and  the  total  insulation  divided  by  two. 

Joint  Testing. — Here  the  length  of  cable  tested  is  very  short 
and,  consequently,  the  resistance  is  enormously  great  so  that 
some  more  delicate  method  than  "  direct  deflection  "  must  be 
employed.  One  of  the  most  convenient  methods  is  that  by 
"  loss  of  charge."  The  connections  are  shown  in  Fig.  42. 

The  condenser  is  first  charged  and  the  discharge  deflection 


INSULATION. 


53 


taken.     It  is  then  charged  and  insulated  with  the  joint  to  be 
tested  submerged  in  water  in  well  insulated  vulcanite  trough  be- 
tween the  poles.     The  deflec- 
tion, after  a  certain  time,  is 
again   taken,   and   difference 
between  this  and  the  first  de- 
flections   shows    the  loss   of 
charge  for  the  given  time. 

The  rate  of  loss  of  charge 
through  a  perfect  joint  is  first 
obtained  for  a  fixed  time,  and 
afterwards  the  loss  of  charge 
for  the  same  time  through  the 
joints  tested  is  compared  to 
this  taken  as  a  standard. 

Another  method  is  to  charge 
the  condenser  for  a  certain 
time  through  a  perfect  core  FIG-  42. 

and  note  the  deflection,  and 
then  charge  it  through  the  joints  to  be  tested. 

An  electrometer  may  also  be  used.  The  quadrants  are 
charged  through  the  joint  and  the  deflection  noted.  This  is 
then  compared  with  a  perfect  core. 

Aerial  Wires.  —  In  this  case,  the  resistances  to  be  measured 
are  usually  comparatively  low,  so  that  if  the  deflection  method 
be  employed  less  elaborate  apparatus  can  be  used,  or  the  deter- 
mination may  be  made  by  the  p.  o.  bridge. 

One  end  of  the  wire  is  joined  to  one  of  the  bridge  terminals, 
the  other  terminal  being  "grounded."  The  other  end  of  the 
wire  should  be  insulated.  The  measurement  can  then  be  made 
in  the  usual  manner.  When  the  deflection  method  is  used,  the 
constant  should  be  obtained  in  ohms  instead  of  meg-ohms. 

The  standard  insulation  of  the  English  Postal  Telegraph  De- 
partment is  200,000  ohms  per  mile.  If  the  resistance  is  below 
this,  the  line  is  considered  faulty. 

The  insulation  per  mile  is  approximately  equal  to  the  total 
insulation  multiplied  by  the  length  in  miles.  It  may  be  ob- 
tained accurately  by  the  formula  : 


= 


Where  i  =  insulation  per  mile,  R^  =  total  resistance  of  line 
with  one  end  insulated,  Re  =  total  resistance  of  line  with  further 
end  grounded,  y  =  the  conductivity  resistance  of  line  per  mile. 


54  ELECTRICAL  MEASUREMENTS. 

It  is  sometimes  required  to  find  the  insulation  resistance  of  two 
sections  of  one  wire  when  it  can  only  be  tested  from  one  end. 

Suppose  A,  c,  to  be  the  wire 

I x 1      which  is  required  to  be  tested 

for  insulation  resistance  from 
_  A  in  two  sections,  A  B  and  B  c. 

A, | C    Let  a  be  the  insulation  resis- 
tance of  the  section,  A,  B,  and 
F1G-  43-  b  that  of  B,  c  ;  and  suppose  x 

to  be  the  insulation  resistance 
of  the  whole  wire  from  A  to  c,  then 

ab 

~^+-j 

from  which 


It  is  only  necessary,  therefore,  in  testing  from  A,  to  get  the  end 
c  insulated  and  measure  the  insulation  resistance,  x.  Then 
get  the  wire  separated  at  B,  the  end  of  the  section,  A,  B,  insu- 
lated and  measure  the  insulation  resistance,  a.  From  these  two 
results  b  can  be  calculated. 


CHAPTER   IX. 


RESISTANCE  OF  TELEGRAPH  LINES,  CABLES,  ETC. 

f  P.  O.  Bridge. 
I  Loop    Test.  |  f 


Equilibrium. 
Mance's  Method. 
Equal  Deflection. 

When  the  conductivity  resistance  of  a  wire  is  to  be  measured 
whose  further  end  is  not  at  hand,  one  end  should  be  joined  to 
one  of  the  terminals  of  a  p.  o.  bridge  while  the  other  bridge  ter- 
minal is  put  to  earth  —  the  other  end  of  the  wire  is  also  put  to 
earth,  and  the  measurement  is  then  made  in  the  usual  way. 

Whenever  possible,  however,  it  is  better  to  measure  without 
using  a  "  ground,"  by  looping  two  wires  together  at  their  further 
ends,  the  nearer  ends  being  joined  to  the  bridge  terminals  ;  this 
gives  the  joint  conductivity  resistance  of  the  two.  Errors  due 
to  earth  currents  or  a  defective  earth,  etc.,  are  thus  avoided. 
The  conductivity  resistance  of  each  wire  separately  cannot  be 
obtained,  however,  by  this  means. 

If  there  be  three  wires  at  hand,  however,  then  the  conduc- 
tivity resistance  of  each  wire  may  be  obtained  by  making  three 
measurements  in  the  following  manner  : 

Let  the  three  wires  be  numbered  respectively  i,  2  and  3. 
First  loop  wires  i  and  2  at  their  further  ends,  and  let  their  re- 
sistance be  R^  ;  next  loop  wires  T  and  3,  and  let  their  resistance 
be  Rz  ;  finally,  loop  2  and  3,  and  let  their  resistance  be  Rz.  In- 
dicating the  resistances  of  i,  2  and  3  by  rlt  rzrz,  we  have  r^  -f- 
rz  =  J?lt  r^  +  rz  =  Rz,  rz  -f  r3  =  J?s.  From  this,  by  adding  the 
equations,  we  get 


2 

and  rs  = 


By  a  method  very  similar  to  the  above,  if  there  be  only  two 
wires  at  hand,  the  resistance  of  the  "  earths  "  at  the  ends  of  the 
lines  may  be  measured  and  also  the  resistance  of  each  wire, 

55 


ELECTRICAL  MEASUREMENTS. 


Denote  the  resistances  of  the  two  wires  by  r±  r^  and  the  re- 
sistances of  the  "  earths  "  by  E. 

First  loop  the  wires,  then  r±  +  rz  =  ^i>  next  "  ground  "  the 
first  wire  and  measure  the  resistance,  then  r±  -j-  E  =  Rz ;  finally, 
ground  the  second  wire,  then  rz  -f-  E  =  fis.  From  these  we  get: 


_  . 


then  E  =  R±  —  R^  rx  =  R±  =  Rz,  and  r2  =  R±  —  Rz. 

Such  a  test,  however,  although  it  eliminates  errors  due  to  de- 
fective earths,  does  not  eliminate  errors  due  to  earth  currents. 

When  it  is  not  possible  to  make  use  of  the  loop  test  and  the 
conductivity,  resistance  of  a  line  of  telegraph  must  be  obtained 
by  "  grounding "  one  end,  the  presence  of  earth  currents  and 
also  currents  due  to  the  polarization  of  the  earth  plates,  renders 
the  Wheatstone  bridge  formula  A  :  B  :  :  R  :  x,  when  equilibrium 
is  produced,  incorrect.  To  obtain  the  true  value  of  the  wire 
resistance  different  methods  and  formulae  are  necessary. 

Equilibrium  Method.— Fig.  44 
shows  the  Wheatstone  bridge 
arrangement,  where  x  =  re- 
sistance of  wire  to  be  deter- 
mined, E  =  E.  M.  F.  due  to  earth 
currents,  etc.,  and  r  =  resis- 
tance of  the  battery  circuit. 

R  is  first  adjusted  to  no  de- 
flection ;  call  this  resistance 
R-L.  The  current  is  then  re- 
versed and  R  readjusted  to  no 
deflection  ;  call  this  resistance 
Rz.  Then  by  applying  KirchhofFs  laws, 


X  =• 

' 


k) 


-  k\ 


where 


=  \  r  ( 


i  + 


Mances  Method.  —  Here  the  current  is  not  reversed  but  the 
values  of  A  and  B  are  changed  and  R  is  again  adjusted  to  no 
deflection.  Call  these  values  A^  B^  R^  and  A2,  Bz,  R%.  In 
practice,  A^  =  B^  and  Az  =  Bz  ;  » 

where  x  __  R±  (2  r  +  A2)  —  Rz  (2  r  -f-  A^ 

(R,  +  A,}  -  (^  +  A,) 

Equal  Deflection  Method.  —  This  is  the  same  as  Mance's  method 
for  the  measurement  of  battery  resistance  except  that  a  battery 


LINES  AND  CABLES.  57 

is  included  in  the  circuit  joining  the  ends  of  the  bridge.  The 
connections  are  shown  in  Fig.  44.  If  there  be  an  earth  current 
the  galvanometer  is  permanently  deflected  if  the  galvanometer 
key  is  kept  closed.  R  is  adjusted  until  on  closing  the  battery  key 
no  change  in  deflection  is  produced.  Then,  A  :  B  :  :  R  :  x. 

In  practice,  it  would  be  necessary  to  short-circuit  the  galvan- 
ometer at  the  moment  when  the  battery  key  is  closed  or  opened, 
otherwise  a  violent  deflection  of  the  needle  would  be  produced 
by  the  static  discharge  from  the  cable. 


CHAPTER  X. 


LOCALIZATION  OF  FAULTS. 

The  conditions  met  with  in  testing  for  the  location  of  faults 
are  so  varied  and  complex  that  it  is  hardly  possible  to  give  any 
general  method  of  procedure.  The  best  way  is  to  consider  each 
of  the  several  cases  separately. 

Faults  may  be  of  the  following  descriptions  : 

t .  Complete  Fault  in  Insulation. 

2.  Partial  Fault  in  Insulation  (Earth  Resistance). 
,   5.    Variable  Fault  in  Insulation  (Polarization  or  Cable  Current]. 
*  4.  Faults  plus  E.  M.  F.  (Earth  Current). 

5.  Fault  in  Conductor. 

6.  Faults  of  High  Resistance. 

(1)  The  simplest  kind  of  fault  to  localize  is  a  complete  frac- 
ture where  the  fault  offers  no  resistance.     Its  position  is  easily 
determined  by  dividing  the  conductivity  resistance  to  the  fault 
by  the  conductivity  resistance  per  mile  of  the  line. 

(2)  When  the  fault  has  a  resistance,  the  localization  becomes 
more  difficult. 

The  following  are  two  theoretical  methods  that  may  be  em- 
ployed. 

Blavier's  Method. — Let  A  B,  Fig.  45,  be  the  line  which  has  a 
fault/ at  c,  A  being  the  testing 
station.  The  end  B  is  first 
insulated  and  the  resistance 
from  A  to  the  fault  measured  ; 
call  this  /.  The  end  B  is  then 
put  to  earth,  and  the  resis- 
tance from  A  again  measured; 
call  this  A .  Then  if  the  con- 
ductivity resistance  of  the  line  be  Z,  and  the  resistance  from  A 
to  c  is  denoted  by  «,  it  may  be  shown  that 

58 


LOCALIZATION  OF  FAULTS.  59 

Dividing  a  by  the  resistance  of  the  line  per  mile  would,  of 
course,  give  the  position  of  the  fault. 

Overlap  Method.  —  In  this  method  two  measurements  are  made, 
one  from  station  A  when  B  is  insulated,  and  the  other  from  B 
when  A  is  insulated. 

Calling  the  first  resistance  /,  the  second  /2  ,  resistance  of  line  L, 
and  the  resistance  from  A  to  the  fault  a,  then 


2 

(3)  The  practical  application  of  the  above  methods,  however, 
presents  considerable  difficulty.     This  is  owing  to  the  variation 
of  the  resistance  of  the  fault  when  the  testing  current  is  put  to 
the  cable,  due  to  electrolytic  action  at  the  fault  which  may  in- 
crease the  resistance  and  also  set  up  a  polarization  current  in 
the  opposite  direction  to  the  testing  current.     This  is  especially 
true  in  the  case  of  sub-marine  cables. 

To  make  a  proper  measurement,  then,  it  is  necessary  to  so 
manipulate  the  testing  apparatus  and  battery  as  to  get  rid  of 
the  polarization  and  resistance  set  up. 

In  Lumsden's  method,  the  further  end  of  the  cable  being  in- 
sulated, the  conductor  is  cleaned  at  the  fault  by  applying  a  zinc 
current  from  100  cells  for  10  or  12  hours,  the  current  being 
occasionally  reversed  for  a  few  minutes.  This  followed  by 
other  special  manipulation. 

In  Fahie's  method,  the  cable  current  is  tested  by  an  auxiliary 
galvanometer.  This  current  is  then  neutralized  with  a  battery. 
If  the  cable  current  is  negative,  a  positive  current  should  be 
used  in  measuring  the  resistance. 

(4)  The  principal  difficulty  in  testing  for  faults  is  the  presence 
of  earth  currents,  especially  in  the  case  of  long  cables.     These 
earth  currents  are  seldom  constant  either  in  strength  or  direc- 
tion for  any  length  of  time. 

Mance's  Method  has  for  its  object  the  elimination  of  the  effects 
of  an  earth  current  in  a  cable  when  making  a  resistance  test. 
The  general  principle  of  this  method  is  the  same  as  that  pre- 
viously described  for  the  measurement  of  the  resistance  of  a 
telegraph  line.  The  bridge  arms  A  and  B  are  made  equal,  and 
then  given  two  different  values,  corresponding  adjustments  be- 
ing made  for  R. 

In  the  Deflection  Method,  the  Wheatstone  bridge  is  not  made 
use  of. 

A  Thomson  galvanometer  with  a  reversing  switch  and  shunt 
and  a  battery  with  reversing  key  are  joined  in  series  with  the 
cable  and  earth.  The  testing  current  is  reversed,  the  galvano- 


6o  ELECTRICAL  MEASUREMENTS. 

meter  being  also  reversed  so  that  the  deflections  may  be  in  the 
same  direction.  Since  in  one  case  the  battery  current  is  in  the 
same  direction  as  the  earth  current,  and  in  the  other  case  it  is 
opposing  it,  the  two  deflections  will  differ.  Call  these  deflections 
dv  and  4-  A  rheostat  is  then  substituted  for  the  cable,  and  the 
resistances  adjusted  until  the  same  deflections  are  produced. 

Call  these  resistances  Rv  and  R% ,  and  X  the  resistance  to  be 
measured  ;  then, 

x  —  ^i  -^i  H-  4  ^2 

4  +  4 

This  method,  of  course,  requires  careful  manipulation. 
When  possible,  the  "  Loop  Test,"  described  below,  should  be 
made  use  of. 

(5)  When  the  conductor  is  broken  inside  the  insulating  sheath- 
ing of  a  cable,  a  battery  joined  to  the  end  of  the  cable  will 
charge  the  latter  up  as  far  as  the  fault  only.     Consequently,  if 
the  discharge  be  measured  and  compared  with  the  discharge 
from  a  condenser  of  known  capacity  charged  fry  the  same  bat- 
tery, the  capacity  of  the  cable  up  to  the  fault  will  be  obtained. 
This  capacity  divided  by  the  capacity  per  mile  of  the  cable  will 
give  the  distance  of  the  fault. 

(6)  In  the  previous  methods  described  for  localizing  faults,  it 
was  assumed  that  the  insulation  resistances  of  the  portions  of 
cable  on  either  side  of  the  fault  were  infinitely  great,  compared 
with  the  resistances  of  the  conductor. 

This  assumption  is  practically  true  when  the  cable  under  test 
is  short,  and  also  if  the  resistance  of  the  fault  is  small  ;  but  in 
the  case  of  long  cables  having  faults  of  high  resistance,  the 
formulae  given  above  are  no  longer  correct. 

The  latter  case  requires  the  use  of  very  complicated  formulae. 

Whenever  possible,  however,  the  loop  test,  with  corrections, 
should  be  employed. 

For  a  complete  discussion  of  the  subject  of  localization  of 
faults,  Kempe's  "  Handbook  of  Electrical  Testing  "  should  be 
consulted. 

The  Loop  Test. — When  a  faulty  cable  is  lying  in  the  tanks  at  a 
factory,  so  that  both  ends  of  it  are  at  hand,  or  when  a  sub- 
merged cable  can  be  looped  at  the  end  farthest  from  the  testing 
station,  with  either  a  second  wire,  if  it  contains  more  than  one 
wire,  or  with  a  second  cable  which  may  be  lying  parallel  with  it, 
then  the  simplest  and  most  accurate  test  for  localizing  the  posi- 
tion of  the  fault  is  the  loop  test. 

This  test  is  independent  (within  certain  limits)  of  the  resis- 
tance of  the  fault. 


LOCALIZATION  OF  FAULTS. 


6l 


There   are   two   ways   of    making   this   test   with    the   P.  o. 
bridge. 

Murray's  Method.  —  (The  connections  are  shown  in  Fig.  46.) 
/  is  the  point  where  the  two 
wires   or    cables   are   looped 
together,  /  being  the  fault. 

Let  x  be  the  resistance 
from  one  end  of  the  bridge 
to  the  fault,  y  the  resistance 
from  the  other  end  of  the 
bridge  to  the  fault.  Then 
the  arm  B  being  plugged  up, 
A  and  R  are  adjusted  until 
equilibrium  is  produced. 
Then,  A  x  y  =  R  X  x. 

Let  L  be  the  total  conduc- 
tivity resistance  of  the  whole 
loop  ;  then,  x  +  y  —  L 


—5  L£— 

Mfc. 


substituting, 


E 

KIG.  46. 

therefore,  y  =  L  —  x  ; 
A  (L  —  x)  =  R  X  x,  from  which  x  =  L   — - . 

A  -}-  R 

Z  may  be  determined  in  the  usual  manner  for  measuring  re- 
sistance. 

A  should  be  given  a  rather  high  value,  say  1,000  ohms,  in 
order  that  the  range  in  adjustment  of  R  may  be  increased. 

The  zinc  current  should  be  put  to  the  cable  (through  the 
bridge). 

The  value  of  x  divided  by  the  conductivity  resistance  of  the 
cable  per  mile  or  foot,  as  the  case  may  be,  gives  the  position  of 
the  fault. 

Farley's  Method. — (Fig.   47    shows   the   arrangement   of   this 

method.)  A  and  B  are  fixed 
resistances,  and  R  is  adjusted 
until  equilibrium  is  produced. 
Then,  B  (R  -f  x)  =  A  7,  and 
y  —  L  —  x  ;  therefore, 
B  (R  +  x)  =  A  (L  —  x),  from 


o 


«i 


B o-. 


'_A 

H'I'H 


which   x  = 


A    L     B    R 


A    +    B 


If 


|-« 


then  A  =  B,  x  = 


L  —  R 


FIG.  47. 


The  conditions  for  making 
this  test  with  accuracy  are  not 
quite  so  simple  as  in  Murray's 


62  ELECTRICAL  MEASUREMENTS. 

method.  In  this  case  they  are  almost  precisely  similar  to 
what  they  are  in  the  ordinary  Wheatstone  bridge  measure- 
ment. 


CHAPTER  XI. 


RESISTANCE  OF  BATTERIES  AND  ELECTROLYTES. 

f  (  Condenser. 

Fall  of  Potential*  \  Hi^h  Resistance. 
Voltmeter.* 


BATTERY  RESISTANCE.      Added  Resistance, 


Mance's  Method. 
Current  and  E.  M.  F.* 

The  resistance  of  a  battery  is  not  a  perfectly  fixed  quantity. 
It  may  vary  somewhat  according  to  the  strength  of  current  that 
is  flowing  and  the  time  that  the  current  has  been  maintained. 
The  resistance  varies  also  with  the  temperature  of  the  battery. 

It  is  therefore  desirable  in  an  accurate  determination  to  know 
the  conditions  of  the  circuit,  especially  the  value  of  the  external 
resistance. 

The  best  method  is  probably  that  by  Fall  of  Potential.  This 
measurement  may  be  carried  out  in  several  ways. 

Condenser  Method. — The  cell  or  battery  x  is  joined  in  series 
with  a  known  resistance  R  and  a  key  b.     Across  the  terminals 
of  the  cell  are  connected  a  con- 
denser, galvanometer  and  dis- 
charge    key,    shown     in     the 
diagram,  Fig.  48. 

The  condenser  is  first  charged 
by  closing  the  key  #,  the  key  b 
remaining  open.  The  con- 
denser is  then  discharged 
through  the  galvanometer. 
The  deflection  thus  obtained, 
;/!,  is  proportional  to  the  E.M.F. 
of  the  cell. 

The  key  b  is  then  closed  and 
the  condenser  again  charged 
and  discharged.  This  deflection,  d% ,  is  proportional  to  the  P.  D. 
across  R.  Therefore  ^  —  dz  is  proportional  to  the  p.  D.  across  x. 
Then :  dl  —  d*  :  d* ,  : :  x  :  R. 


FIG.  48. 


64  ELECTRICAL  MEASUREMENTS. 

If  R  be  varied  until  4  =  — *,  then  R  =  x. 

2 

R  may  be  given  different  values,  and  the  corresponding1  values 
of  x  determined,  or  x  may  be  measured  after  the  current  has 
been  flowing  for  different  lengths  of  time. 

This  method  is  especially  applicable  when  the  efficiency  of 
any  particular  cell  is  to  be  investigated. 

High  Resistance  Method.—  A  galvanometer  and  high  resistance 
may  be  substituted  in  place  of  the  condenser.  The  high  resis- 
tance is  joined  in  series  with  the  galvanometer,  and  readings 
are  taken  across  the  terminals  of  the  cell  similar  to  those  in  the 
above  method.  The  calculation  is  the  same. 

Voltmeter  Method. — A  low  reading  voltmeter,  such  as  the  Weston 
voltmeter,  that  can  be  read  directly  to  ^  volt  and  estimated  to 

^^^  volt,  may  be  used  to  take 
the  deflections  across  the  cell. 
Readings  are  made  with  the 
key  open  and  with  the  key 


closed,  in  the  same  manner  as 
in  the  condenser  method,  and 
the  same  calculation  is  used. 

If  R  is  adjusted  until  the  de- 
flection  with   the  key   closed 
FIG>  49>  is  one-half   of   the   deflection 

with  the  key  open,  then  R  is  equal  to  the  resistance  of  the  cell. 

This  method  is  to  be  recommended  for  all  ordinary  deter- 
minations of  cell  resistance. 

It  is,  of  course,  inapplicable  in  the  case  where  the  resistance 
of  a  battery  is  appreciably  great  compared  to  the  resistance  of 
the  voltmeter. 

Tangent  Galvanometer  Method. — If  a  low  resistance  tangent 
galvanometer  be  at  hand,  the  determination  can  be  made  in  the 
following  manner  :  Take  the  deflection  with  the  cell  and  galva- 
nometer in  series,  call  this  deflection  4 ,  and  the  resistance  of 
the  circuit  x.  Then  add  a  known  resistance,  R,  preferably  such 
that  will  about  halve  the  deflection,  call  this  4-  Then  : 

x  :  x  +  R  : :  tan  4  '  tan  dlt 

and        x  —  galvanometer  resistance  =  the  cell  resistance, 
assuming  the  resistance  of  the  leads  to  be  negligible. 

This  method  may  sometimes  be  found  convenient  for  a  labor- 
atory determination  where  the  cell  is  fairly  constant. 

If  a  low  resistance  reflecting  galvanometer  be  used  and  the 
resistance  neglected,  and  such  a  resistance,  R,  added,  that 
d  =  — 1  ,  then  R  =  the  battery  resistance. 


BATTERY  RESISTANCE.  65 

If  the  battery  has  a  fairly  high  resistance  and  the  galvano- 
meter resistance,  G,  is  not  neglible,  then  the  following  method 
may  be  used  :  The  galvanometer,  battery  and  a  rheostat  are 
joined  in  series.  The  resistance,  RX,  is  adjusted  until  some  con- 
venient deflection  is  obtained.  Then  the  resistance  is  increased 
until  the  deflection  is  halved  ;  call  this  second  resistance  R2 . 
Then: 

R  =  R2  —  (2  RI  +  G), 

where  R  is  the  resistance  of  the  battery. 

Mance's  Method. — In  this  method,  the  cell  is  joined  to  the 
terminals  of  a  Wheatstone  bridge,  in  place  of  the  unknown  re- 
sistance, the  ends  of  the  bridge  being  connected  by  a  wire  fur- 
nished with  a  key.  The  connections  are  the  same  as  those 
shown  in  Fig.  44,  except  that  no  testing  battery  need  be  em- 
ployed. The  position  of  the  cell  is  indicated  by  x. 

The  galvanometer  key  is  closed  and  the  steady  deflection  pro- 
duced by  the  cell  is  reduced  to  some  convenient  amount  either 
by  lowering  the  magnet,  if  the  Thomson  galvanometer  is  used, 
or  by  the  addition  of  an  extra  resistance  to  the  galvanometer 
circuit.  R  is  then  adjusted  until  no  change  is  produced  in  the 
deflection  on  closing  the  key  joining  the  ends  of  the  bridge. 
The  manipulation  in  this  method  is  sometimes  rather  difficult, 
and  it  is  hardly  to  be  recommended  when  fall  of  potential  me- 
thods can  be  employed. 

Current  and  E.  M.  F. — In  some  instances,  where  the  internal 
resistance  of  a  cell  is  very  low,  the  P.  D.  across  an  external  re- 
sistance subtracted  from  the  E.  M.  F.  of  the  cell  gives  such  a 
small  difference,  that  measurements  cannot  be  made  accurately 
by  fall  of  potential  methods. 

In  this  case,  it  is  best  to  measure  the  current  with  an  ammeter 
and  the  E.  M.  F.  with  a  voltmeter ;  then  the  resistance  can  be 

E> 

calculated  from  the  formulae  R  =  — . 

RES,STANCE  OF  E.BCTKO..VTE,  {  %£%%?£„,«. 

When  the  resistance  of  a  fluid,  which  is  decomposed  by  the 
current,  is  to  be  measured,  account  must  be  taken  of  the  oppos- 
ing E.  M.  F.  of  polarization.  The  simplest  method  is  that  of 
substitution. 

The  fluid  is  placed  in  a  U  tube  provided  with  platinum  elec- 
trodes, one  arm  of  the  tube  being  calibrated. 

The  fluid  thus  contained  is  included  in  a  simple  circuit  with  a 
rheostat,  a  galvanometer  and  a  galvanic  cell. 


66 


ELECTRICAL  MEASUREMENTS. 


FIG.  50. 


The  arrangement  is  shown  in  Fig.  50. 

The  position  of  the  needle  is  then  observed  when  so  much  of 
the  column  of  fluid  is  included  that  the  deflection  is  a  conveni- 
ent amount ;  then  one  electrode 
is  approached  to  the  other  by 
the  length  /,  and  such  an 
amount  R  of  rheostat  resistance 
thrown  into  the  circuit  that  the 
same  deflection  is  produced- 
The  resistance  -R  is  then  equal 
to  that  of  the  fluid  between  the 
two  positions  of  the  movable 
electrode,  assuming  the  polar- 
ization to  be  the  same  in  both 
cases.  It  is  well  to  use  spirals 
of  platinum  wire  or  platinum  gauze  for  the  electrodes. 

Since  the  conductivity  of  fluids  varies  greatly  with  their  tem- 
perature, this  should  be  observed,  and  be  kept  constant  by 
placing  the  tube  in  a  water-bath  provided  with  a  thermometer. 
The  influence  of  polarization  may  be  avoided,  and  the  resis- 
tance of  an  electrolyte  measured  directly,  just  as  that  of  a  me- 
tallic conductor,  if  a  rapidly  alternating  current  be  employed. 

The  tube  containing  the  fluid,  x,  is  joined  to  the  terminals  of 
a  Wheatstone  bridge,  the  current  being  furnished  by  an  induc- 
tion coil.  A  telephone  receiver  is  used  in  place  of  the  galvano- 
meter. The  connections  are 
shown  in  Fig.  51.  The  ad- 
justment to  equilibrium  is 
obtained  when  the  telephone 
gives  the  minimum  sound, 
then  A  :  B  : :  R  :  x.  A  num- 
ber of  observations  should  be 
made. 

The  electrodes  in  this  case 
should  consist  of  platinized 
platinum  foil. 

To  obtain  the  "Specific 
Resistance "  of  a  fluid,  the 
containing  vessel  should  first 
be  filled  with  mercury,  and 
the  resistance  measured  in  the  usual  way.  This  gives  the 
"mercury  constant"  of  the  vessel.  This  resistance  divided 
into  the  resistance  of  the  fluid  gives  its  resistance  compared  to 
mercury,  from  which  the  resistance  compared  to  copper  can  be 


RESISTANCE  OF  ELECTROLYTES.  67 

calculated.  If  the  dimensions  of  the  containing  vessel,  or  rather 
the  column  of  fluid  measured,  were  accurately  known,  then  the 
resistance  of  unit  volume  could  be  calculated. 


CHAPTER  XII. 


INCANDESCENT  LAMPS,  "  DYNAMO 
RESISTANCE,"  ETC. 

It  is  often  required  to  measure  the  resistances  of  incandes- 
cent lamps  or  arc  lamps  while  running.  The  resistance  of  an 
incandescent  lamp  depends  very  largely  upon  the  temperature 
of  the  filament,  and  consequently  upon  the  strength  of  current 
flowing.  It  is  therefore  desirable  that  the  original  conditions 
of  the  circuit  be  interfered  with  as  little  as  possible  when  the 
measurement  is  made. 

The  fall  of  potential  across  the  lamp  may  be  measured  with 

a  voltmeter,  and  then  the  p.  D. 
across  a  small  resistance,  such 
as  an  ohm,  in  series  with  the 
lamp  (Fig.  52).  The  resis- 
tance is  then  calculated  by  a 
direct  proportion. 

In  place  of  the  voltmeter,  a 
galvanometer  and  high  re- 
sistance oragalvanometerand 


FIG.  52.  condenser  can  be  employed. 

The  series  resistance  should  be  of  such  size  wire  that  it  will 
not  be  heated  appreciably  by  the  current,  and  the  resistance 
should  be  small  compared  to  that  of  the  lamp,  so  that  the  cur- 
rent will  not  be  materially  reduced  by  it. 

A  better  practical  method,  however,  is  to  measure  the  current 
flowing  through  the  lamp  with  an  ammeter  (an  instrument  hav- 
ing a  negligibly  small  resistance),  and  the  fall  of  potential  across 
the  lamp  with  a  voltmeter.  The  resistance  is  then  calculated 

E> 

from  the  formula  R  —  —. 

O 

The  resistance  can  also  be  measured  directly  by  means  of  an 
ohmmeter.  In  principle,  the,  ohmmeter  consists  of  two  coils  at 
right  angles  to  each  other,  with  a  small  needle  at  the  point  of 
intersection  of  the  axis  (Fig  53).  One  of  the  coils  of  low  resis- 
tance is  in  series  with  the  resistance  to  be  measured,  and  the 
other,  which  is  of  comparatively  high  resistance,  is  in  shunt. 


DYNAMO  RESISTANCE.  69 

Under  these  circumstances  the  action  of  the  needle  is  due  to 
the  ratio  of  the  difference  of  potential  at  the  terminals  of  the 
unknown  resistance  and  the  current  strength  in  the  series  coil, 


The  coils  are  so  proportioned,  that  when  the  current  flows 
through  the  short  thick  wire,  it  moves  the  needle  to  the  zero  of 
the  scale,  while  the  long  thin  wire  of  the  shunt  coil  produces  a 
deflection  directly  proportional  to  the  resistance. 

If  the  coils  are  large  and  the  needle  short,  the  instrument  will 
follow  the  tangent  law. 

In  Eve'rshed's  ohmmeter,  the  current  coils  are  wound  outside 
and  the  shunt  or  pressure  coil  is  globular  in  form,  so  as  to  fit 
inside.  It  is  placed  at  an  angle  of  45  °,  so  as  to  give  a  long  scale. 
Inside  the  shunt  coil  a  hard  steel  needle  is  suspended  by  a  silk 
fibre.  A  second  needle  is 
hung  outside  the  coils,  so  that 
the  instrument  is  astatic. 

The  range  of  the  instru- 
ment is  increased  by  insert- 
ing resistance  in  series  with 
the  shunt  coil.  It  is  gradu- 
ated by  experiment. 

An  ohmmeter  should  al- 
ways be  tested  to  see  if  it  is 
accurate.  A  piece  of  thick 
wire  is  measured  in  the  or- 
dinary  way,  and  the  resistance 
then  determined  with  an  ohmmeter.  Care  must  be  taken  that 
the  wire  does  not  become  heated.  The  same  resistance  should 
be  measured  with  a  large  current  and  a  small  current. 

The  apparent  resistance  of  a  dynamo,  while  running  may  be 
determined  in  the  following  manner  :  A  voltmeter  being  con- 
nected across  the  terminals,  the  P.  D.  is  measured  on  closed 
circuit.  This  gives  the  fall  of  potential  across  the  external  resis- 
tance, or  the  P.  D.  across  the  "  line  ".  The  current  should  also 
be  measured  with  an  ammeter. 

The  circuit  then  being  opened,  the  voltmeter  indicates  the 
total  P.  D.  that  the  dynamo  is  capable  of  giving. 

The  first  reading  subtracted  from  this  shows  the  P.  D.  across 
the  dynamo  when  running  on  the  above  circuit.  The  resistance 

can  then  be  obtained  from  the  formula  R  —  —      Of  course,  if 

u 

the  resistance  of  the  external  circuit  were  known,  the  resistance 
of  the  dynamo  could  be  calculated  without  using  the  ammeter. 


CHAPTER  XIII. 
DETERMINATION  OF  THE  OHM,  CONSTRUCTION  OF  STANDARDS,  ETC. 


The  measurement  of  resistance  consists  of  the  comparison  of 
the  resistances  to  be  determined  with  some  other  resistance 
taken  as  a  standard. 

The  derivation  and  determination  of  this  standard  is  of  inter- 
est, though,  of  course,  its  absolute  determination  is  never  re- 
quired in  practice. 

That  originally  taken  as  a  convenient  unit  was  approximately 
the  resistance  of  a  mile  of  copper  wire  of  a  certain  size.  An 
exact  value  was  assigned  to  it  by  Siemens,  who  defined  it  as  the 
resistance  of  a  column  of  mercury  one  metre  in  length  and  one 
square  millimetre  in  section  at  the  temperature  of  melting  ice. 
This  has  been  called  the  Siemens  unit. 

With  the  application  of  the  c.  G.  s.  system  to  electrical 
measurement  and  the  adoption  of  the  magnetic  definitions,  the 
unit  of  resistance  was  defined  as  the  ratio  of  the  centimetre  to 
the  second.  The  product  of  this  quantity  by  io9,  called  the  ohm, 
was  designed  for  practical  use,  the  c.  G.  s.  unit  being  incon- 
veniently small.  It  has  nearly  the  same  value  as  the  Siemens  unit. 

The  exact  determination  of  this  unit  has  been  the  work  of 
many  years.  The  original  B.  A.  ohm  of  1864  has  been  replaced 
by  more  accurate  determinations  of  the  c.  G.  s.  unit.  The  Paris 
Conference  in  1884  agreed  upon  the  so  called  legal  ohm,  and 
defined  the  resistance  as  that  of  a  column  of  mercury,  106  centi- 
metres long,  of  one  square  millimetre  section,  at  the  tempera- 
ture of  melting  ice. 

At  the  British  Association  meeting  of  1892,  the  results  of  a 
large  number  of  independent  measurements  were  compared, 
and  what  is  now  known  as  the  international  ohm  or  the  true 
ohm  was  adopted. 

Its  resistance  is  defined  as  that  of  14. 45  21*  grammes  of  mer- 
cury in  the  form  of  a  column  of  uniform  cross  section  106.3 
centimetres  in  length  at  o°  C.  (It  is  equivalent  to  a  cross- 
section  of  one  square  millimetre). 

The  above  value  was  also  adopted  by  the  Electrical  Congress 
at  Chicago  in  1893. 

Table  I.  shows  the  relative  values  of  the  different  units. 


STANDARDS  OF  RESISTANCE. 


An  outline  of  the  general  method  followed  in  the  absolute  de- 
termination is  indicated  below. 

A  coil  of  wire  of  known  area  and  number  of  turns  is  placed 
so  that  the  axis  of  the  coil  is  in  the  magnetic  meridian,  and 
rotated  with  a  known  velocity.  By  definition  the  c.  G.  s.  unit  of 
E.  M.  F.  is  that  obtained  when  one  "  line  of  force  "  is  cut  per 
second,  and  hence  the  E.  M.  F.  developed  by  the  coil  can  be  cal- 
culated. Let  F  =  the  total  strength  of  field  ;  then  since  each 
line  of  force  is  cut  four  times 
in  one  revolution  of  the  coil, 
the  E.M.F.  =area  of  coil  X  num- 
ber of  turns  X  4  X  F  x  num- 
ber of  revolutions  per  second. 
The  coil  is  joined  in  series  with 
a  tangent  galvanometer  (Fig. 
54),  and  the  current  strength 
obtained  by  the  formula 

C=  —  X  H  X  tan^, 

2  H  7T 

where  B  =  deflection,  R  =  ra- 

dius  of  galvanometer  coils,  and  n  =  number  of  turns. 

The  resistance  of  the  circuit  can  then  be  calculated  from  the 

Tf 

formula  R  =  — . 

TABLE  I. 


» 

Siemens 
Unit. 

B.  A.  Ohm. 

Legal  Ohm. 

International 
Ohm. 

Siemens  Unit 

I  OO 

•9535 

•9434 

.9407 

B.  A   Ohm     
Legal  Ohm  

1.0488 
i.c6 

I.OO 

1.0107 

.9894 

I.OO 

.9866 
.9972 

International  or  True  Ohm  

1.063 

1.0136 

1.0028 

.1.00 

FIG.  55. 


If  a  resistance  be  added  to  the  circuit,  the 
above  operation  may  be  repeated  and  the 
resistance  of  the  circuit  again  obtained. 

The  difference  between  these  two  results 
would  give  the  value  of  the  resistance  added. 

Since  the  resistance  is  measured  in  c.  G.  s. 
units,  it  must  be  divided  by  io9  to  reduce  it 
to  ohms. 

The  secondary  standards  consist  of  coils  of 
wire  of  various  alloys,  whose  resistance  are 
known  to  be  very  nearly  constant. 

A  form  of  standard  resistance  coil  devised 
for  the  first  British  Association  committee, 
and  which  was  till  recently  the  generally  ac- 
cepted form,  is  shown  in  Fig.  55. 


?2  ELECTRICAL  MEASUREMENTS. 

It  consists  of  a  coil  of  wire  on  a  metal  bobbin  with  a  tubular 
core,  the  ends  being  connected  to  a  pair  of  thick  copper  rods, 
led  through  ebonite  clamps,  and  bent  downwards  so  as  to  be 
easily  put  into  mercury  cups. 

The  whole  coil  is  then  slipped  into  an  outside  case  of  thin 
sheet  metal  in  the  form  of  two  cylinders.  The  lower  cylinder 
contains  the  wire  coil,  and  the  upper  is  filled  with  paraffin  wax. 
The  case  up  to  the  shoulder  is  intended  to  be  placed  in  a  bath 
of  water,  the  temperature  of  which  is  taken  with  a  thermometer 
placed  in  the  central  tube  after  the  coil  has  been  so  long  in  the 
bath  that  it  has  reached  the  temperature  of  the  water. 

The  coils  of  a  rheostat  should  be  wound  bifilar  (Fig.  56)  to 

neutralize  the  magnetic  action 
of  the  current  and  prevent  ef- 
fects due  to  self-induction. 
This  winding  is  most  easily 
accomplished  from  two  bob- 
bins, the  farther  ends  of  the 
wire  being  soldered  together. 
The  coils  should  be  dipped 
in  melted  paraffin  to  secure 
6  more  perfect  insulation  and 

prevent  any  atmospheric  ac- 
tion on  the  wire  that  might  change  the  resistance  in  the  course 
of  time. 

The  following  are  the  principal  materials  that  have  been 
employed  commercially  for  constructing  resistances. 

German  silver,  an  alloy  of  copper,  nickel,  and  zinc.  Specific 
resistance  about  18,  but  varies  greatly,  according  to  the  compo- 
sition of  the  alloy.  Temperature  coefficient  .04  per  cent,  per 
i°  C.  Largely  used  in  the  construction  of  rheostat  coils. 

Platinum  silver,  composed  of  two  parts  by  weight  of  platinum 
to  one  of  silver.  Specific  resistance  about  15.  Resistance  in- 
creases .031  per  cent,  per  degree  centigrade.  Used  for  standards. 
Platinoid  is  German  silver  with  the  addition  of  a  small  per- 
centage of  tungsten.  Specific  resistance  about  17.  Temperature 
coefficient  .022  per  degree  centigrade. 

Manganin,  specific  resistance  about  20.  Alloys  containing 
manganese  have  been  found  to  have  very  small  temperature 
coefficients,  and  it  is  even  possible  to  obtain  them  with  negative 
coefficients.  In  the  case  of  this,  or  any  of  the  new  alloys,  a  long 
series  of  observations  are  required  to  establish  with  any  degree 
of  certainty  the  permanency  of  the  resistance. 


CHAPTER  XIV. 


Electromotive  Force  and  Potential  Difference, 
Measurement  of  E.  M.  F.  of  Batteries  and  Direct  Currents. 

The  term  "  electromotive  force  "  is  not  a  scientifically  accurate 
one,  since  in  the  Newtonian  sense,  force  is  only  that  which  acts 
on  matter. 

This  restricted  use  of  the  term  "  force,"  however,  does  not 
seem  advisable  when  the  present  state  of  scientific  theories  with 
regard  to  the  ether  is  considered.  It  would  be  better  if  force 
were  defined  as  that  which  produces  or  tends  to  produce  motion, 
or  that  which  produces  stress. 

It  may  be  well  to  consider  briefly- the  possible  nature  of  elec- 
trical action,  in  order  to  show  more  clearly  the  relation  between 
electromotive  force  and  potential  difference. 

Suppose  some  cause,  an  electromotive  force,  produces  a  stress 
in  the  ether.  This  stress,  under  certain  conditions,  produces 
an  ether  strain  or  displacement,  and  the  change  from  stress  to 
strain  must,  of  course,  be  accompanied  by  motion,  either  vibra- 
tional  or  progressive. 

This  motion -is  known  as  an  electric  current.  Its  presence 
can  only  be  recognized  when  the  ethereal  motion  has  been  con- 
vected  into  jthe  motion  of  the  grosser  particles  of  matter. 

Since  the  same  effect  may  be  produced  by  different  causes, 
though  any  given  cause  must  always  produce  the  same  effect, 
potential  difference  may  be  due  to  a  great  variety  of  electro- 
motive forces. 

We  may  then  define  electromotive  force  as  the  cause  which 
produces  potential  difference,  and  potential  difference  as  that 
which  produces  or  tends  to  produce  an  electric  current. 

From  the  above  considerations  it  seems  to  the  writer  that  the 
term  "  electromotive  force  "  is  a  particularly  good  one  ;  it  is 
only  its  mode  of  use  that  should  be  objected  to. 

It  is  evident  that,  strictly  speaking,  electromotive  force  can 
never  be  measured  ;  it  is  only  potential  difference  that  may  be 

determined.     It  should  also  be  remembered  that  in  the  state- 

iy 

ment  of  Ohm's  law,  C  =  — ,  that  the  E  stands  for  difference  of 

R 

potential,  and  not  electromotive  force. 

'      73 


74 


ELECTRICAL  MEASUREMENTS. 


BATTERIES  AND 
DIRECT  CURRENTS. 


There  has  been  a  great  want  of  uniformity  in  the  employment 
of  the  term  "  electromotive  force-"  By  some,  it  is  regarded  as 
that  which  causes  difference  of  potential ;  others  consider  it  as 
being  produced  by  potential  difference  ;  and  still  others  regard 
it  as  the  entire  electric  moving  cause  produced  by  any  source  ; 
while  anything  less  than  this  is  called  potential  difference.  This 
last  distinction  between  the  two  terms  is  that  ordinarily  used 
with  regard  to  dynamos  and  batteries. 

Whenever  the  term  " electromotive  force"  (E.  M.  F.)  is  used 
with  respect  to  measurements,  it  should  be  understood  to  indi- 
cate "  total  potential  difference." 

The  abbreviation  T.  p.  D.  has  been  suggested  in  place  of  E.  M.  F. 
Its  employment  would  save  much  confusion. 

f  I  Deflection  and  Resistance, 

j  High  Resistance  Method  *\  Equal  Deflection. 

(  Equal  Resistance. 
Wheatstone's  Method. 
Lumsderi's  Method. 
Condenser  Method.* 

(  Five  Arc  (Cushman). 
Potentiometer* •]  Quadruplex  (Muirhead). 

(  Duplex  (Varley). 
Current  and  Resistance. 
Electrometer. 
Voltmeter  * 

For  the  determination  of  potential  difference  (P.  D.)  in  direct 
current  and  battery  work,  a  great  variety  of  methods  may  be 
selected  from.  The  more  important  of  these  are  indicated  in 
the  above  classification.  Of  course,  the  most  exact  measure- 
ment is  obtained  by  means  of  the  potentiometer,  but  other  me- 
thods are  often  better  suited  for  special  cases. 

High  Resistance  Method. — If  a  source  of  potential  difference, 
for  example  the  battery  EX  ,  is  joined  in  series  with  a  galvano- 
meter and  a  resistance  (Fig.  57),  the 
E.  M.  F.  is  proportional  to  the  deflection 
di  X  RI,  where  RJ  equals  the  entire  resis- 
tance of  the  circuit,  for  from  Ohm's  law 
E=  CR. 

1  R  I : — *— J  '         Let  another  battery  E2  be  used  in  place 

of  E!  ,  then  the  E.  M.  F.  is  proportional  to 
4  X  R2,  where  dz  equals  the  deflection, 


FIG.   57. 


and  R2  the  entire  resistance  in  circuit.  >v. 

Hence,  EJ  :  E2  :  :  dl  RX  :  4  R  . 

The  difficulty  with  this  method  is  that  it  requires  the  resis- 
tance of  the  batteries  and  galvanometer  to  be  known. 

A  modification  of  the  above  is  to  vary  the  resistance  in  circuit 
until  the  two  deflections  are  equal. 

Then,  EJ  :  E2  : :  RX  -:  R2. 


MEASUREMENT  OF  E.  M.  F. 


75 


If  the  resistance  in  circuit  is  equal  in  both  cases,  then 

E!  :  Eg  :  :  </!  :  </2 . 

This  is  accomplished  in  practice  by  making  the  resistance  R  so 
great  that  the  battery  resistances,  rl  and  r2,  are  negligibly  small 
compared  to  it.  Then  the  E.  M.  F.  is  directly  proportional  to  the 
deflection. 

A  sensitive  reflecting  galvanometer  should  be  used,  and  the 
resistance  R  ought  not  to  be  less  than  10,000  ohms,  a  resistance 
of  100,000  ohms  being  preferable. 

Wheatstones  Method. — In  this  method,  the  battery  EI  is  joined 
up  in  series  with  a  galvanometer  and  rheostat ;  a  deflection  dl  is 
obtained.  The  resistance  is  now  increased  by  R!  ,  so  that  the 
deflection  is  reduced  to  </2 .  The  battery  E2  is  next  used  in  place 
of  Et ,  and  the  resistance  in  circuit  is  adjusted  until  the  deflection 
obtained  equals  dv .  The  resistance  is  now  increased  by  R2 ,  so 
that  the  deflection  is  reduced  to  dz ,  as  in  the  first  instance  ;  then 

EI  :  E2  :  :  Rr  :  R2 . 

That  is,  the  E.  M.  F.'S  are  directly  proportional  to  the  added  re- 
sistances. 

Lumsderis  Method. — This  method  may  sometimes  be  found  con- 
venient in  comparing  the  E.  M.  F.  of  battery  cells. 

The  two  batteries  EI  ,  E2  are  joined  up, 
with  their   opposite    poles   connected    to- 
gether, and  with  resistances  RI  ,  R2 ,  in  cir- 
cuit (Fig.  58);  a  galvanometer  is  connected 
between  the  points  gl  g2 .     One  of  the  re- 
sistances, say  R!,  being  fixed,  the  other,  R2, 
is  adjusted  until  the  galvanometer  gives 
no  deflection  ;  then  EI  :  E2  :  :  RX  :  R2 . 
The  method  of  making  the  connections  when  a  P.  o.  bridge  is 
used,  is  shown  in  Fig.  59. 

If  in  place  of  making  Rt  equal  to  1,000  ohms,  it  be  made  some 
multiple  of  EX,  then  when  R2  is  adjusted  so  that  no  deflection 
is  obtained,  it  must 
be  equal  to  the  same 
multiple  of  E2.  Thus, 
suppose  Et  =  1.44 
volts,   R!   =    1,440 
ohms,  then  if  R2  = 
1,079  ohms.  £2=1.079 
volts. 

The  above  adjust- 
ment could  be  made 
by  removing  the  a 


FIG.   58. 


r 


100° 


FIG.   59. 


76  ELECTRICAL  MEASUREMENTS. 

peg  between  posts  a  and  £,  and  interpolating  a  resistance  of  440 
ohms,  the  galvanometer  with  an  extra  key  in  circuit  being 
joined  to  the  post  b. 

Condenser  Method. — One  of  the  most  convenient  as  well  as  one 
of  the  most  universally  applicable  methods  is  that  in  which  the 
condenser  is  used.  The  resistance  of  the  condenser  is  practi- 
cally infinite  as  far  as  any  other  resistance  in  circuit  is  con- 
cerned, so  that  the  E.  M.  F.  of  batteries,  whose  internal  resistance 
is  very  great,  can  be  accurately  determined  by  this  method. 
Again,  there  is  not  the  slightest  chance  for  any  polarization 
effects  to  take  place  during  the  measurement. 

The  connections  are  shown  in  Fig.  60.  When  the  discharge 
key  K  is  depressed,  points  i  and  2  are 
connected,  the  condenser  F  being  charged 
by  the  battery  E:.  When  the  points  i 
and  3  are  connected,  the  condenser  is 
discharged  through  the  galvanometer. 
The  deflection  d±  is  proportional  to  the 


capacity  of  the  condenser  F  X  E|. 

Another  battery,  E2,  is  joined  up   in 
place  of  E!,  and  the  throw  of  the  galvano- 
meter 4  again  obtained,  and  since  this  deflection  is  proportional 
to  F  X  E2 ,  we  have  : 

EJ   :  E2  :  :  dl   :  4  • 

That  is,  the  E.  M.  F.'S  are  directly  proportional  to  the  galvano- 
meter deflections. 

Potentiometer  Method. — This  method  is  the  standard  for  the 
accurate  comparison  of  E.  M.  F.'S,  such  as  the  checking  of  stan- 
dard cells  against  each  other,  and  also  for  the  calibration  of 
voltmeters. 

It  admits  of  the  very  greatest  precision  of  adjustment,  and  is 
a  zero  method,  that  is,  it  does  not  depend  on  galvanometer  de- 
flections. Moreover,  this  method  is  practically  a  static  one,  for 
when  the  final  balance  is  obtained,  there  is  no  flow  of  current 
from  the  branch  circuit  containing  the  cell  to  be  tested.  Thus 
the  measurement  is  not  effected  by  the  internal  resistances  of 
the  cells  or  batteries  compared,  however  high,  and  is  also  un- 
influenced by  the  addition  of  any  resistance  that  may  be  placed 
in  series  with  them  to  prevent  polarization  during  the  first  ad- 
justments. 

The  method  depends  on  the  law,  that  if  a  source  of  p.  D.  be 
joined  to  the  ends  of  a  resistance,  the  p.  D.  across  any  portion  of 
the  resistance  is  proportional  to  the  resistance  itself.  Also,  if 
the  ends  of  a  second  circuit  with  a  given  E.  M.  F.  be  joined  by  a 


POTENTIOMETER.  77 

portion  of  the  above  resistance,  such  that  the  p.  D.  across  it  is 
equal  to  this  E.  M.  F.  and  in  the  opposite  direction,  there  will  be 
no  flow  of  current  from  the  second  circuit. 

The  connections  are  shown  in  the  diagram,  Fig.  61. 
A  constant  battery  B,  whose  E.  M.  F.  is  somewhat  greater  than 
that  to  be  determined,  is  joined  to  the  ends  of  a  resistance  R  R1  , 

so  arranged  that  the  portion  R  included 
B|j[i|j[j    _        between    the    galvanometer    terminals 

gz  may  be  varied  until  the  P.  D.  across 
-g  just  equa]  to  tjie  E  M   F  0£  the  ce|| 

I       E,  shown  by  no  deflection  of  the  galvano- 


j/u  ,  - 

8      B  #  meter.     This  may  be  accomplished  by 

*         I  employing  a  bridge  wire  and  varying 

r—  |  _  j     x-x  the  position  of  the  galvanometer  slider, 

I5~vl/  ^2,  until  there  is  equilibrium.     For  most 

work,  however,  it  is  better  that  this  re- 
sistance should  be  high,  at  least  10,000 

ohms,  so  in  place  of  the  bridge  wire  two  rheostats  may  be  used 
in  the  positions  indicated  by  R  and  R1.  The  sum  of  these  resis- 
tances R  and  R1  must  be  kept  equal  to  10,000  ohms,  that  is,  when- 
ever R  is  increased,  R1  must  be  decreased  by  the  same  amount, 
and  vice  versa. 

A  far  more  convenient  arrangement  is  to  employ  one  of  the 
slide  coil  bridges,  known  as  "potentiometers,"  previously  de- 
scribed. The  positive  pole  of  the  battery  is  joined  to  the  zero 
terminal  of  the  potentiometer,  and  the  negative  to  the  opposite 
terminal.  The  positive  pole  of  the  cell  to  be  tested  is  also 
joined  to  the  zero  terminal,  and  the  negative  to  the  slider  or 
key,  ^2)  through  the  galvanometer. 

The  reading  of  the  potentiometer,  when  adjusted  to  no  deflec- 
tion, shows  the  value  of  R,  and  the  entire  resistance  of  the  po- 
tentiometer is  equal  to  R  -f  RI  . 

r  is  a.  resistance  placed  in  series  with  the  cell  E,  to  prevent 
polarization  during  the  trial  adjustments,  and  may  -be  short- 
circuited  before  the  final  adjustment. 

s1  is  a  shunt  resistance  joined  to  the  terminals  of  the  battery, 
in  order  to  reduce  the  p.  D.  across  R  R1  to  any  given  amount,  and 
need  only  be  used  when  it  is  desired  to  make  the  potentiometer 
direct  reading. 

The  determination  is  made  in  the  following  manner  :  A  cell  E 
of  known  E.  M.  F.  is  first  used,  and  the  value  of  R  found  when 
there  is  no  deflection.  A  second  cell,  EI?  is  then  substituted 
the  value  of  R,  again  found  when  there  is  equilibrium.  Call  this 
second  value  of  R  equal  to  Rt  .  Then, 
E  :  E  :  :  R  :  R  . 


ELECTRICAL  MEASUREMENTS. 


FIG.  62. 


The  value  of  R  and  RX  are  given  directly  by  the  potentiometer 
reading's. 

In  the  comparison  of  standard  cells,  great  care  should  be 
taken  that  they  are  of  the  same  temperature  and  several  read- 
ings should  be  made. 

To  make  the  potentiometer  direct  reading,  a  cell  of  known 
E.  M.  F.,  say  1,434  volts,  is  used,  and  R  is  made  equal  to  it,  in  this 
case  1,434.  s1  is  then  adjusted  until  the  galvanometer  shows  no 
deflection.  Then  if,  when  another  cell  is  used,  R  is  found  equal 
to  1,078,  the  E.  M.  F.  would  be  1.078  volts. 

Current  and  Resistance. — This  method  is  of  special  use  in  check- 
ing standard  cells  and  voltmeters. 

In  the  diagram,  B  is  a  constant  battery,  R  a  known  resistance, 
say  10  ohms,  the  wire  being  large  enough 
not  to  be  heated  appreciably  by  the  cur- 
rent. A  is  a  current  measuring  device, 
such  as  a  voltameter,  Thomson  balance,  or 
calibrated  ammeter,  s1  is  an  adjustable  -i 
resistance.  E  is  the  standard  cell  to  be 
checked  in  series  with  a  galvanometer, 
and  r  is  a  resistance  to  protect  the  cell 
from  polarization.  The  key  being  closed, 
s1  is  adjusted  until  the  galvanometer  gives  no  deflection  and  the 
current  c  is  measured.  Then,  E  =  p.  D.  across  R  =  R  c. 

If  a  voltmeter  is  to  be  checked,  it  is  joined  across  R,  and  the 
reading  E  taken  with  the  key  closed,  the  current  c  being 
measured  at  the  same  time. 

If  the  voltmeter  is  correct,  of  course  E  should  equal  R  c. 
Electrometer. — The  E.  M.  F.  of   cells   can  be  quite   accurately 
compared   with   the   Thomson    quadrant    electrometer,  if  the 
needle  be  given  a  static  charge  and  the  cell 
terminals    connected  to  alternate  pairs   of 
quadrants,  Fig.  63.     The  cell  is  then  con- 
nected and  the  deflection  read  ;  call  this  d. 
Another  cell,  E1 ,  is  substituted  and  the  de- 
flection dl  measured.     Then, 
E  :  E1  :  :  d  :  dl. 

A  circular  scale  should  be  used.  It  is  diffi- 
cult to  keep  the  needle  at  a  constant  po- 
tential unless  a  replenisner  is  employed 
and  external  electric  charges  are  apt  to  effect  the  measure- 
ment. 

The  method  is  not  to  be  recommended  except  for  research 
work. 


VOLTMETER. 


79 


Voltmeter. — In  a  very  great  number  of  cases,  the  voltmeter  is 
by  far  the  most  convenient  means  of  measuring  p.  D. 

A  large  class  of  voltmeters,  practically  all  that  are  used  for 
direct  current  and  battery  work,  are  really  current  instruments  ; 
thac  is,  the  deflection  is  produced  by  the  current  flowing  through 
the  instrument.  The  scale,  however,  is  calibrated  to  indicate 
the  P.  D.  across  the  terminals  of  the  voltmeter.  The  higher  the 
resistance  of  the  voltmeter,  the  more  nearly  will  it  give  the  true 
p.  D.  in  any  case  where  it  is  used  in  series,  and  the  less  will  it 
tend  to  disturb  the  relation  of  the  circuit  when  it  is  used  in 
parallel.  An  example  may,  perhaps,  make  this  plainer.  Sup- 
pose a  battery  has  a  resistance  of  100  ohms  and  an  E.  M.  F.  of  125 
volts,  and  a  voltmeter  with  2,000  ohms  resistance  is  used.  Then 

the  voltmeter,  if  correct,  would  indicate  2'000  X  125  =  119  volts. 

2,100 

It  is  therefore  well  to  know  the  conditions  of  the  circuit  and 
the  resistance  of  the  voltmeter  in  any  particular  measurement. 

The  portable  and  laboratory  forms  of  the  Weston  voltmeter 
are  well-known  standard  instruments  and  may  be  thoroughly 
relied  upon  to  indicate  correctly  the  p.  D.  across  ther  terminals. 
Fig.  64  gives  an  idea  of  their  construc- 
tion. 

The  principle  is  that  of  the  D'Arsonval 
galvanometer.  The  magnet  is  placed  hor- 
izontally, and  the  coil,  in  an  oblique  posi- 


FIG.  64. 


tion  between  the  pole  pieces,  turns  in 
jeweled  bearings.  The  current  is  lead  in 
by  means  of  watch  springs.  Two  resis- 
tance coils,  J?,  r,  are  placed  in  series  with 
the  movable  coil.  With  R  in  series,  the 
resistance  in  some  of  the  instruments  is 
about  15,000  ohms,  and  scale  reads  in  volts 
up  to  150.  With  r  in  series,  the  resistance  is  about  500  ohms, 
and  scale  indicates  %\  volt  up  to  5  volts. 

In  order  to  change  the  reading,  it  is  only  necessary  to  ,use  a 
different  terminal. 

The  instrument  is  also  provided  with  a  commutator. 

The  following  is  a  list  of  some  of  the  more  important  forms 
of  voltmeter,  though,  of  course,  nearly  any  device  used  for  am- 
meter may  be  employed  for  a  voltmeter,  if  it  be  given  a  suffici- 
ently high  resistance. 


8o 


ELECTRICAL  MEASUREMENTS. 
VOLTMETERS. 


EUctrostattc  Voltmeter 

ELECTROSTATIC      I 

INSTRUMENTS.    ,  Multicellular — spring. 


CURRENT 

INSTRUMENTS.  "> 


Low  Reading  Voltmeter . 

(  f  Direct  Current  Voltmeter— 

We*ton\  \      sPring~  magnet. 

•']  Alternating    Current    Volt- 
i      meter— dynamometers. 

Ayrton^  Perry's j$I™et. 


Thomson's  Graded  Galvanometers — magnet. 
Magnetic  Vane— spring. 
Eversheds — gravity. 
[  Cardew— expansion. 


CHAPTER  XV. 


E.  M.  F.  OF  ALTER-  (  Measurement  of  Very  High  E.  M.  F.  and  Very  Low 
NATING  CURRENTS.  \     E.  M.  F. 

E.  M.  F.  of  Alternating  Currents.  —  The  E.  M.  F.  of  alternating 
currents  may  be  conveniently  measured  by  the  following  in- 
struments : 

Electrostatic  Voltmeter* 


ELECTROMETER.  \   Multicellular* 
I    Quadrant. 
[  Low  Reading. 

DYNAMOMETER.  \    w,eston^s  *  (Alternating  Current  Voltmeter.) 
Stetnen  s. 

ATTRACTION  OR      (  Hartman  and  Braun's. 
ELECTRO-MAGNETIC  •<  Evershed's. 

VOLTMETERS.        (  Magnetic  Vane,  etc 

CALORIC  VOLTMETER  (Car  dew's.} 


The  form  of  electrometer  known  as  Thomson's  Electrostatic 
Voltmeter  is  very  largely  used  in  alternating  current  work. 

The  construction  is  shown  by  the  diagram 
Fig.  65. 

A  light  aluminium  vane  is  pivoted  on 
knife  edges  between  two  brass  plates  and 
is  carefully  insulated  from  them.  The  vane 
is  provided  with  a  pointer  and  to  the  lower 
end  of  the  vane  small  counter  weights  may 
be  added.  The  terminals  of  the  source  of 
p.  D.  are  connected  to  the  brass  plates  and 
the  movable  vane,  the  attraction  is  then 
proportional  to  the  pTlx2.  The  scale  is 
graduated  in  divisons  proportional  to  po- 
tential differences.  Three  counter  weights 
are  provided  and  according  to  which  is  used 
the  scale  divisions  are  equal  to  50  volts,  100  volts,  or  200  volts 
respectively.  The  range  of  the  instruments  is  thus  very  large, 

Si 


FIG.  65. 


82 


ELECTRICAL  MEASUREMENTS. 


but  it  is  liable  to  spark  if  more  than  10,000  volts  are  used.  It  is 
provided,  however,  with  a  safety  fuse. 

In  the  Multicellular  Electrometer,  Fig.  66,  a 
number  of  movable  vanes  are  employed  turn- 
ing between  corresponding  fixed  plates.  The 
force  of  attraction  is  balanced  by  the  torsion  of 
the  wire  suspending  the  vanes.  The  scale  is 
graduated  directly  to  volts. 

The  instrument  is   made   in   four   different 
ranges,  giving  readings  from  40  to  800  volts. 
It  is  possible  with  this  form  of  electrometer  to          FlG  66 
read  as  low  as  15  volts. 

The  ordinary  Thomson  Quadrant  Electrometer  may  be  used 
to  measure  an  alternating  E.  M.  F.  if  the  vane  and  one  pair  of 
quadrants  be  joined  to  a  terminal  from  the  source  of  p.  D.  and 
the  other  terminal  connected  to  the  opposite  pair  of  quadrants. 
The  connections  are  then  reversed  by  means  of  a  commutator 
and  the  deflection  observed.  The  E.  M.  F.'S  are  then  proportional 
to  2  A/deflections. 

This  form  of  instrument  is  somewhat  difficult  to  use  and  re- 
quires considerable  care  in  the  adjustments. 

A  special  form  of  electrometer  in  which  the  moving  vane  is 
rectangular  in  shape  and  suspended  by  a  fine  wire,  is  known  as 
the  "Low  Reading  Electrometer."  By  means  of  a  lamp  and 
scale,  it  is  possible  that  as  low  an  E.  M.  F.  as  -^  volt  can  be  meas- 
ured with  this  instrument. 

The  employment  of  some  form  of  electrometer,  whenever 
possible,  is  to  be  most  strongly  recommended. 

Since  it  measures  p.  D.  entirely  by  electrostatic  pressure,  its 
use  produces  no  change  in  the  relations  of 
the  circuit,  and  if  the  scale  is  graduated 
correctly  it  must  indicate  the  true  poten- 
tial difference. 

The  dynamometer  consists  of  a  fixed  and 
a  movable  coil  of  wire,  the  latter  being 
normally  at  an  angle  to  the  plane  of  the 
former,  Fig.  67,  and  both  coils  being 
traversed  by  the  current  whose  E.  M.  F.  is 
to  be  measured. 

Directive  force  may  be  given  to  the 
movable  coil  either  by  the  elasticity  of  a 
spring  or  the  torsion  of  a  suspending  wire. 

The  deflections  of  the  movable  coil  are  proportional  to  the 
square  of  the  current  strength,  and  consequently  to  the  square 
pf  the  E.  M.  F. 


ALTERNATING  E.  M.  F.'S.  83 

fastened  to  an  axle  provided  with  a  counter  weight  and  indica- 
ting hand,  is  placed  with  the  coil  to  one  side  of  the  axis.  When 

When  a  current  passes  through  the  coils,  an  attraction  is 
exerted,  and  the  movable  coil  tends  to  take  a  position  parallel 
to  the  plane  of  the  fixed  coil. 

Change  of  direction  of  the  current  in  the  entire  instrument 
does  not  alter  the  direction  of  the  deflection,  and  hence  it  is 
suitable  for  alternating  work. 

For  small  E.  M.  F.'S  the  dynamometer  is  not  very  sensitive, 
since  the  deflection  is  proportional  to  the  square  of  the  E.  M.  F. 

For  determination  of  E.  M.  F.  the  coils  should  be  given  a  high 
resistance,  or  a  high  resistance  should  be  placed  in  series  with 
them. 

The  Weston  alternating  current  voltmeter  is  a  form  of  dyna- 
mometer in  which  the  movable  coil  is  mounted  in  bearings  and 
the  current  lead  in  by  watch  springs  fastened  to  the  axle,  the 
arrangement  being  similar  to  that  described  in  the  direct  cur- 
rent voltmeter.  This  instrument  is  quite  sensitive  and  the 
readings  reliable.  It  is  extremely  useful  for  all  ordinary 
measurements  of  alternating  E.  M.  F.'S  It  is  possible,  however, 
that  the  readings  may  be  slightly  effected  by  the  action  of 
strong  magnetic  fields. 

In  a  form  of  the  Siemen's  dynamometer,  the  attraction  be- 
tween the  coils  is  measured  by  the  angle  of  torsion  of  an  elastic 
spring,  by  turning  the  torsion  circle  of  which  the  deflected  coil 
is  brought  back  to  zero.  The  E.  M.  F.  is  then  proportional  to 
the  square  root  of  the  angle  of  torsion.  The  axis  of  the 
movable  coil  should  be  North  and  South,  so  that  it  may  not  be 
effected  by  terrestial  magnetism. 

A  large  class  of  voltmeters  which  may  be  called  attraction  or 
electro -magnetic  voltmeters  depend  on  the  principle  that  when  a 
current  flows  through  a  coil  of  wire  it  creates  a  magnetic  field 
which  attracts  a  piece  of  soft  iron  towards  the  strongest  portion 
of  the  field. 

This  attraction  is,  of  course,  independent  of  the  direction  of 
the  current. 

In  a  form  of  instrument  manufactured  by  Hartman  and 
Braun,  a  small  soft  iron  coil  is  held  by  means  of  a  spring  just 
above  the  attracting  coil,  and  the  motion  is  multiplied  by  means 
of  a  lever  arm  moving  over  a  graduated  scale. 

One  form  of  the  Ayrton  and  Perry  voltmeter  is  similar  to  the 
above,  except  that  the  spring  is  placed  within  the  coil  and  the 
arrangement  of  the  indicating  hand  is  somewhat  different. 

In  Evershed's  voltmeter,  Fig.    68,   a  piece  of  soft  iron,  s  s, 


ELECTRICAL  MEASUREMENT^. 


FIG.     68. 


a  current  flows  through  the  coil  it  tends  to  rotate  the  soft  iron 
core  to  a  position  in  the  axis  of  the  coil. 

In  the  magnetic  vane  voltmeter,  the 
p.  D.  is  measured  by  the  repulsion  exerted 
between  a  fixed  and  movable  vane  of  soft 
iron  placed  in  the  field  of  a  magnetizing 
coil,  the  action  of  the  movable  vane  being 
opposed  by  a  spring. 

Just  what  errors  may  be  caused  by  hyster- 
esis or  residual  magnetism  in  the  above 
class  of  voltmeters  it  is  difficult  to  say,  but  it  is  probable  that 
most  of  them  are  fairly  correct  and  well  adapted  to  the  class 
of  measurements  for  which  they  are  employed. 

It  should  be  understood  that  the  instruments  just  described 
may  be  employed  as  voltmeters  or  ammeters,  depending  on 
whether  they  are  given  a  high  or  a  low  resistance. 

Caloric  voltmeter.  When  a  current  flows  through  a  wire,  the 
wire  is  heated  and  expands.  The  amount  of  heating  or  expan- 
sion is  proportional  to  the  current  and  also  to  the  p.  D.  across 
the  ends  of  the  wire. 

In  the  "  hot  wire  "  voltmeter,  the  amount  of  this  expansion  is 
indicated  by  a  pointer  held  in  position  by  springs,  the  scale  be- 
ing graduated  in  volts.    Fig.  69,  shows  the 
principle  of    construction  of  the  instru- 
ment. 

In  the  Cardew  voltmeter  as  formerly 
manufactured,  the  expansion  wire  was 
placed  in  a  long  tube  at  the  side  of  the 
indicating  scale.  In  the  more  recent  in- 
struments, however,  a  circular  case  is  em- 
ployed and  their  appearance  does  not 
differ  from  the  ordinary  voltmeter. 

The  expansion  of  the  wire  is,  of  course, 

independent  of  the  direction  of  the  current.  The  readings  are 
not  effected  by  strong  magnetic  fields,  and  hence  these  instru- 
ments are  very  suitable  for  station  work. 

Some  of  these  instruments,  however,  have  a  rather  low  re- 
sistance and  require  a  considerable  current  to  operate  them,  so 
that  they  are  not  always  adapted  to  measurements  when  the  re- 
sistance of  the  voltmeter  is  a  factor  in  the  determination. 

Measurement  of  very  high  E.  M.  F. — The  Thomson  Electrostatic 
Voltmeter  might  be  employed  for  the  determination  of  E.  M.  F.'S 
considerably  above  10,000  volts  if  the  distance  between  the 
plates  and  the  vane  were  made  sufficiently  great  to  prevent 


FIG.  69. 


VERY  HIGH  E.  M.  F.'S.  85 

sparking  and  if  the  entire  instrument  were  very  carefully  in- 
sulated. Heavier  counter  weights  could  be  employed  and  each 
division  deflection  thus  made  to  correspond  to  a  greater  p.  D. 

In  the  Absolute  Electrometer  and  Kirchhoff's  Balance,  the 
attraction  between  a  fixed  and  movable  plate  is  measured  and 
by  means  of  suitable  formula  the  E.  M.  F.  calculated.  Of  course, 
the  limit  of  measurement  is  determined  by  the  striking  distance 
of  the  spark  and  by  the  insulation  of  the  apparatus. 

Very  great  potential  differences  can  be  roughly  calculated 
from  the  striking  distance  of  the  spark  in  air.  It  depends  to 
a  certain  extent  on  the  size  and  shape  of  the  electrodes.  The 
striking  distance  increases  faster  than  the  difference  of  poten  • 
tial,  and  the  curve  indicating  the  ratios  of  striking  distances  to 
differences  of  potential  is  a  parabola. 

According  to  Lord  Kelvin's  measurements,  the  potential  dif- 
ference required  to  produce  a  spark  in  air,  between  parallel 
plates,  and  of  a  given  length,  diminishes  rapidly  as  the  distance 
increases,  approaching  a  limiting  value  of  30,000  volts  per  centi- 
metre, which  may  be  assumed  constant  for  distances  greater 
than  one  centimetre. 

For  sparks  not  under  two  millimetres  in  length  the  volts  ne- 
cessary to  start  a  spark  across  a  length  of  /  centimetres  may  be 
approximately  calculated  by  the  formula — 
V  =  1,500  -j-  30,000  /. 

Measurement  of  very  low  E.  M.  F. — A  very  sensitive  galvano- 
meter will  give  a  deflection  of  one  scale  division  for  a  differ- 
ence of  potential  of  .00000  r  volt  across  its  terminals. 

The  galvanometer  may  be  calibrated  by  means  of  a  standard 
cell  in  series  with  a  high  resistance.  Thus:  suppose  the  resist- 
ance used  is  100,000  ohms,  galvanometer  resistance  1000  ohms, 
and  deflection  300  divisions,  then  i  division  deflection  =  1,435 

volts  X  — — =  .000047  volt. 

ioi,coo  X  300 

With  one  form  of  the  Weston  voltmeter  readings  as  low  as 
3-jj-g-  volt  can  be  obtained,  and  if  the  series  resistance  were  cut 
out  it  is  probable  that  it  would  indicate  about  3^^  volt. 

Quite  small  differences  of  potential  may  be  observed  by  means 
of  a  capillary  electrometer,  which  consists  of  a  very  finely  drawn 
out  glass  tube  containing  mercury  and  60  per  cent  sulphuric 
acid  in  contact  with  each  other.  A  potential  difference  between 
them  causes  a  change  of  capillary  pressure  at  the  point  of  con- 
tact, and  hence  a  displacement,  which  for  small  potential  differ- 
ence is  proportional  to  the  latter.  This  displacement  may  be 
accurately  determined  by  means  of  a  microscope. 


CHAPTER  XVI. 


CALIBRATION  OF  VOLTMETERS  AND  STANDARD'S  OF  E.  M.  F. 


FIG.    70 


Voltmeters  are  best  calibrated  by  comparison  with  one  or 
more  standard  cells  by  means  of  a  potentiometer.  The  arrange- 
ment of  the  experi- 

B 


ment  is  shown   in  the 
diagram  Fig.  70. 

Across  the  ends  of 
the  potentiometer  RR', 
consisting  of  a  slide 
coil  bridge  similar  in 
construction  to  one  of 
the  forms  previously 
described  and  of  not 
less  than  10,000  ohms 
resistance,  is  joined  the 
voltmeter  v. 

In  place  of  a  slide  coil  bridge  two  rheostats  may  be  employed 
for  R  and  R'  and  the  adjustments  so  made  that  the  joint  resist- 
tance  is  always  10,000  ohms.  A  battery  of  constant  cells  B,  pre- 
ferably storage  cells,  with  a  shunt  resistance  s'  is  also  connected 
to  the  terminals  of  the  potentiometer.  The  E.  M.  F.  of  this  bat 
tery  should  be  somewhat  greater  than  the  highest  reading  of  the 
voltmeter.  The  standard  cells  E  in  series  with  a  protecting  re- 
sistance r,  thac  may  be  short-circuited,  and  the  galvanometer  are 
joined  to  one  terminal  of  the  potentiometer  and  the  contact  key 
as  slider.  The  positive  poles  of  testing  battery  and  standard 
cells  should  be  connected  to  the  zero  terminal  of  the  potentio- 
meter. 

If  it  is  desired  to  find  the  errors  in  a  voltmeter  scale  already 
graduated  the  method  is  as  follows:  s'  is  adjusted  until  some 
convenient  reading  is  obtained  on  the  voltmeter,  and  then  a 
balance  is  obtained  on  the  potentiometer,  shown  by  no  deflec- 
tion of  the  galvanometer,  the  potential  difference  v  across  the 
ends  of  the  potentiometer  being  calculated  from  the  proportion. 

86 


VOLTMETER  CALIBRATION.  87 

R  :  R  -|-  R '  :  :  E  :  v.  Example,  voltmeter  reading  =  10.7,  E  =  1.435 
X  2,  R  =  2657,  R  -|-  R'  =  10,000  ;  then  2657  :  10,000  :  :  2.87  :  v. 
v  =  10.8  volts  ;  error  of  voltmeter  reading  is  therefore  —  o.  i 
volt  and  the  correction  -f-  o.i  volt. 

By  this  means  the  errors  in  various  parts  of  the  scale  are  de- 
termined and  a  correction  table  or  curve  constructed. 

When  it  is  desired  to  graduate  the  scale  or  adjust  the  volt- 
meter by  changing  its  resistance  until  the  readings  correspond 
with  the  scale,  the  following  method  is  employed.  Suppose  a 
potential  difference  of  exactly  10  volts  is  required  across  the 
voltmeter  terminals,  R  is  given  such  a  value  that  R  :  R  -f-  R'  :  : 
E  :  10,  thus  R  :  10,000  :  :  2.87  :  10,  R  =  2870.  s'  is  then  adjusted 
until  the  galvanometer  gives  no  deflection.  The  potential  dif- 
ference across  the  potentiometer  and  consequently  across  the 
voltmeter  must  then  be  just  10  volts.  The  position  taken  by 
the  indicating  hand  of  the  voltmeter  is  therefore  marked  10, 
and  so  on  for  the  other  portions  of  the  scale. 

The  advantage  of  using  several  standard  cells  is  that  a  better 
average  value  for  the  E.  M.  F.  is  obtained  and  also  that  the  read- 
ings on  the  potentiometer  are  larger,  when  the  potential  differ- 
ences across  the  terminals  are  high,  than  if  a  single  cell  were 
employed.  For  very  accurate  work  the  standard  cells  should  be 
placed  in  a  water  bath  or  an  oil  bath,  and  the  correction,  if  any, 
for  the  temperature  coefficient  applied. 

It  should  be  understood  that  the  above  method  is  suitable  for 
the  calibration  of  standard  laboratory  voltmeters.  After  a  volt- 
meter has  once  been  accurately  calibrated,  other  voltmeters 
may  be  checked  by  a  direct  comparison  with  it. 

A  voltmeter  may  also  be  checked  by  taking  the  reading  across 
a  known  resistence  R  through  which  a  known  current  C  is  flow- 
ing. The  potential  difference  E  across  R  may  then  be  calculated 
from  the  formula  E—  C  R.  The  difference  between  this  and  the 
voltmeter  reading,  of  course,  gives  the  correction.  The  arrange- 
ment is  similar  to  that  shown  in  Fig.  62  except  that  the  volt- 
meter terminals  are  joined  across  R  in  place  of  the  cell  E,  galva- 
nometer, etc.  By  varying  the  current  different  readings  may 
be  obtained.  For  R,  a  standard  ohm  or  some  accurately  measured 
resistance  that  will  not  be  heated  by  the  current  should  be  em- 
ployed. This  resistance  should  be  low  compared  to  the  volt- 
meter resistance.  The  current  can  be  measured  by  means  of  a 
Thomson  balance,  a  calibrated  ammeter,  or  if  it  be  constant,  with 
a  voltmeter. 

Standards  of  E.  M.  E. — In  the  case  of  E.  M.  F.,  there  is  consi- 
derable difference  in  the  values  of  the  unit  and  of  the  standard. 


88  ELECTRICAL  MEASUREMENTS. 

The  "  absolute  unit "  of  E.  M.  F.  is  the  E.  M.  F.  developed  by  a 
conductor  when  it  cuts  one  "line  of  force"  per  second.  The 
practical  unit  or  volt  is  io8  absolute  units.  The  international 
standard  of  E.  M.  F.  adopted  is  the  Clark  standard  cell.  Its  E.  M. 
F.  is  1.434  true  volts  at  i5Qc.  It  consists  of  an  anode  of  pure 
zinc  in  a  concentrated  solution  of  zinc- sulphate  and  a  cathode  of 
pure  mercury  in  contact  with  a  paste  of  pure  mercurous  sul 
phate.  Precise  directions  are  given  for  setting  up  these  cells, 
and  if  the  directions  are  followed  they  may  be  relied  upon  to 
give  the  E.  M.  F.  stated  above.  The  variations  of  the  E.  M.  F.  with 
temperature  may  be  calculated  with  sufficient  accuracy  from  the 
formula  : 

E  =  i-434  ! i  —  0.00077  (/—is);, 

where  t  is  the  temperature  of  the  cell  in  degrees  centigrade. 

Various  other  standard  cells  are  made  use  of  in  practice.  The 
Carhart-Clark  cell  employs  a  solution  of  zinc-sulphate  saturated 
at  o°c.  Its  E.  M.  F.  is  1.440  true  volts  at  i5°c.  and  the  tempera- 
ture coefficient  is  approximately  0.00038  per  degree  c. 

In  the  Weston  standard  cell,  a  cadmium  anode  is  used  im- 
mersed in  sulphate  of  cadmium.  The  E.  M.  F.  is  1.025  true  volts 
and  this  value  is  practically  constant  at  all  ordinary  tempera- 
tures. 

Standard  Clark-cells  prepared  according  to  the  specifications 
are  best  checked  by  comparison  with  each  other  by  the  poten- 
tiometer method,  care  being  taken  that  they  are  of  the  same 
temperature.  If  several  are  found  to  agree  to  the  third  decimal 
place,  it  may  be  taken  as  very  certain  that  the  E.  M.  F.  is  1.434 
true  volts  at  i5°c.  Other  standard  cells  may  then  be  compared 
with  them  by  the  same  method. 

The  E.  M.  F.  of  standard  cells  may  also  be  determined  by  con- 
necting in  series  with  a  galvanometer  and  protecting  resistance 
and  joining  the  terminals  of  this  branch  circuit  across  a  known 
resistance  R  through  which  a  current  from  a  constant  battery  is 
flowing.  The  arrangement  of  the  experiment  is  shown  in  Fig. 
62.  The  current  is  varied  by  means  of  the  resistance  s'  until 
the  potential  difference  across  R  is  equal  to  the  E.  M.  F.  of  the 
standard  cell  shown  by  no  deflection  of  the  galvanometer.  The 
current  can  be  measured  accurately  by  means  of  a  silver  volt- 
meter or  by  use  of  a  Thomson  Balance.  Then  E  =  c  R. 

It  may  be  well  to  state  that  the  E.  M  F.  differs  according  as  it 
is  expressed  in  true  or  international  volts,  legal  volts,  or  B.  A. 
volts.  The  ratios  are  the  same  as  those  existing  between  the 
the  corresponding  values  of  the  ohm. 


CHAPTER  XVII. 
CURRENT. 


The  presence  of  an  electrical  current  is  manifested  by  several 
accompanying  phenomena  and  it  is  by  the  observation  of  the 
intensity  of  these  phenomena  that  current  strength  is  deter- 
mined. 

A  conductor  carrying  a  current  is  surrounded  by  a  magnetic 
field,  and  the  strength  of  this  field  may  be  measured  by  the  de- 
flective action  on  a  magnetic  needle,  the  attractive  force  exerted 
on  a  piece  of  soft  iron,  the  attraction  between  two  coils  through 
which  the  current  is  flowing,  etc. 

Besides  this  magnetic  field  there  is  also  an  electrostatic  field 
surrounding  the  conductor,  in  other  words,  there  is  a  difference 
of  potential  all  along  a  conductor  through  which  a  current  is 
flowing.  This  potential  difference  can  be  determined  and  the 
resistance  across  which  it  is  measured  being  known,  the  current 
may  be  calculated. 

Whenever  a  current  flows  through  a  conductor  heat  is  devel- 
oped and  this  calorific  effect  is  proportional  to  the  square  of  the 
strength  of  the  current. 

If  a  current  be  made  to  flow  through  an  electrolyte,  chemical- 
action  takes  place  and  this  chemical  action  is  also  a  measure  of 
the  current  strength. 

The  methods  and  instruments  for  the  measurement  of  current 
are  quite  numerous  and,  of  course,  vary  according  to  the  special 
cases  required. 

One  method,  however,  is  universally  applicable.  This  is  the 
measurement  of  the  potential  difference  across  a  known  resist- 
ance. For  this  determination  any  of  the  methods  used  for  the 
measurement  of  P.  D.  can  be  employed. 

It  may,  perhaps,  be  found  more  convenient  at  times  to  make 
use  of  some  of  the  other  methods,  so  it  is  well  to  briefly  consider 
them. 

89 


ELECTRICAL  MEASUREMENTS. 


DIRECT 
CURRENTS. 


(  Direct  Method. 

E.  M.  F.  and  Resistance..  \  Differential  Method  (Cardew's). 
(  Bridge  Method  (Kempe's). 


P.  D.  and  Resistance. 


Tangent  Galvanometer. 


f  Direct  Deflection  Method. 

|  Equilibrium  Method. 

-{  Potentiometer  Method. 
Voltmeter  Method.* 
Galvanometer  Method.* 


]  ^eight. 


Ammeter.* 


(  Also  the  methods  given  for  Alternating 
(       Currents. 

E.  M.  F.  and  resistance,  direct  method. — To  measure  current  by 
this  method  the  deflection  of  a  low  resistance  galvanometer  is 
noted  when  placed  in  the  circuit  through  which  flows  the  current 
whose  strength  is  to  be  determined.  The  galvanometer  is  then 
joined  in  series  with  a  battery  of  known  E.  M.  F.  and  a  rheostat, 


FIG.  71.  FIG.  72. 

the  resistance  being  adjusted  until  the  deflection  is  equal  to 
that  obtained  in  the  first  case.  Then  the  current  may  be  cal- 
culated from  the  formula 

C    '-  R+G  +  r    ' 

Where  G  =  resistance  of  galvanometer  and  r  =  resistance  of 
battery.  These  latter  may  be  neglected  if  small  compared  to  R, 
This  method  is  applicable  to  the  measurement  of  compara- 
tively weak  currents. 

Cardew's  Differential  Method. — For  this  method  the  galvano- 
meter is  wound  with  two  coils  g  g^  Fig.  71.  Through  the  coil^, 
which  is  of  low  resistance,  is  passed  the  current  to  be  measured. 
To  the  other  coil  g  is  joined  a  cell  of  known  E.  M.  F.  and  a  re- 
sistance JR.  This  resistance  is  adjusted  until  there  is  no  deflec- 
tion, then 


MEASUREMENT  OF  CURRENT. 

where  </and  d±  are  respectively  the  relative  deflective  effects  of 
the  coils  g  and  glt  The  values  of  d  and  d±  may  be  determined  by 
joining  up  a  battery  and  two  resistances  Rl  and  R%  in  the  man- 
ner shown  in  Fig.  72,  and  then  adjusting  until  equilibrium  is 

7  T>  I 

produced  ;  then    —  —     l    '   ^ 

Kempe's  Bridge  Method. — This  method  is  a  modification  of  the 
preceding  one,  and  has  the  advantage  that  it  does  not  require  a 
special  form  of  galvanometer. 

In  making  the  measurement  the  resistance  R,  Fig.  73,  is  ad- 
justed until  no  deflection  is  observed,  then 

Er 


where  Cl  is  the  current  to  be  measured  and  E  the  E.  M.  F.  of  the 
auxiliary  cell  whose  resistance  should  be  negligible  compared 
to  R.  It  is  well  to  give  the  resistances  r  and  rlt  a  ratio  of  say 
100  :  i. 

IOO 


Example  :  C,  =  — ['°8  X , 

i  (4000  -f-  100) 


=  .026. 


—  V 


FIG.  74. 


FIG.  73- 

P.  D.  and  Resistance. — The  p.  D.  across  a  known  resistance 
through  which  a  current  is  flowing  may  be  determined  in  a 
great  variety  of  ways  and  from  this  the  value  of  the  current 
is  readily  calculated. 

If  a  galvanometer  in  series  with  a  high  resistance  R,  Fig.  74, 
be  joined  across  a  low  resistance  r  through  which  a  current  is 
flowing  and  the  deflection  d^  observed,  and  then  if  the  galvano- 
meter and  high  resistance  be  joined  up  with  a  cell  E  of  known 
E.  M.  F.  and  the  deflection  d  read,  the  P.  D.  across  r>  V  —  Vly  is 
obtained  from  the  proportion  V —  V^\  E  \  \  d^\  d. 

A  galvanometer  and  cell  E  of  a  known  E.  M.  F.  can  be  con- 
nected across  r  and  this  resistance  varied  until  equilibrium  is 
obtained,  then  E  —  V —  V^  It  is  evident  that  such  a  method 
would  only  be  applicable  in  special  cases.  A  potentiometer 
might  be  employed  to  measure  the  p.  D.  where  considerable 
accuracy  was  required.  The  p.  D.  could  also  be  determined  by 
charging  a  condenser  across  /-. 


92  ELECTRICAL  MEASUREMENTS. 

One  of  the  most  convenient  and  accurate  methods  of  measur- 
ing current  is  to  employ  a  Weston  voltmeter  with  a  low  reading 
scale  across  a  shunt  R  through  which  the 
AVZ current  is  flowing,  Fig.  75.    Then  if  E  be 


the  voltmeter  reading,  C  =  — -. 

R 

It  is  well  to  have  a  set  of  shunts  of 
"*"  say  the  following  values,  .001,  .01,  o.  i,  i. 
FJG  ohm  respectively.  The  low  resistances 

to  be  used  for  heavy  currents  and  the 
higher  resistances  for  light  currents. 

Where  very  small  currents  are  to  be  measured,  a  high  resist- 
ance galvanometer  should  be  joined  across  a  i-ohm  shunt, 
through  which  the  current  flows,  and  the  deflection  observed. 
The  value  of  the  galvanometer  deflection  per  scale  division  in 
microvolts  can  afterwards  be  obtained  by  means  of  a  standard 
cell  and  high  resistance.  Since  the  best  galvanometers  have  a 
sensitiveness  of  i  microvolt,  it  is  possible  to  measure  current 
to  the  one-millionth  of  an  ampere  with  a  one-ohm  shunt. 

The  strength  of  current  that  can  be  determined  by  this 
method,  when  voltmeters  and  shunts  of  very  low  resistance  are 
employed,  is,  of  course,  practically  unlimited. 

Tangent  Galvanometer. — If  the  diameter  of  the  coils  of  a  gal- 
vanometer is  great,  compared  to  the  length  of  the  needle,  the 
tangent  of  the  angle  of  deflection  is  proportional  to  the  current 
flowing  through  the  instrument. 

The  same  effect  may  be  obtained  by  placing  the  coils  sym- 
metrically each  side  of  the  needle.  For  strong  currents,  a  sin- 
gle turn  of  very  thick  copper  wire  should  be  employed. 

The  "  constant "  of  the  galvanometer,  or  the  amount  of 
current  necessary  to  produce  i°  deflection,  depends  on  the  ra- 
dius of  the  coils,  number  of  turns,  and  strength  of  field.  The 
value  of  this  constant  can  be  obtained  by  observing  the  de- 
flection with  a  battery  of  known  E.  M.  F.  and  a  known  resist- 
ance in  circuit,  or  by  comparison  with  a  voltmeter,  calibrated 
ammeter,  standard  voltmeter  across  shunt,  etc. 

The  tangent  galvanometer  gives  a  ready  means  for  the  com- 
parison of  current  strengths,  but  the  use  of  the  ammeter  or 
shunted  voltmeter,  for  most  work,  is  much  to  be, preferred. 

Voltameters.— According  to  the  resolutions  adopted  by  the 
Electrical  Congress  of  1893,  the  international  ampere  is  con- 
sidered as  represented  sufficiently  well  for  practical  use  by  the 
unvarying  current  which,  when  passed  through  a  solution  of 
nitrate  of  silver  in  water,  and  in  accordance  with  the  specifica- 


MEASUREMENT  OF  CURRENT.  93 

tions  given,  deposits  silver  at  the  rate  of  0.001118  of  a  gramme 
per  second. 

A  neutral  solution  of  pure  silver  nitrate,  containing  about  15 
per  cent,  by  weight  of  the  nitrate  and  85  per  cent,  of  water 
should  be  employed.  A  current  strength  of  about  one  ampere 
should  be  used  and  the  specifications  strictly  followed  if  the 
most  accurate  results  are  desired. 

The  value  of  the  current  can  be  obtained  from  the  formula, 
C  =  Weight  of  silver  deposited  -=-  (0.001118  X  Time  in  seconds). 

For  approximate  work  a  voltameter  consisting  of  copper  in  a 
solution  of  copper  sulphate  may  be  employed.  An  ampere  will 
then  deposit  0.0003281  of  a  gramme  of  copper  per  second. 

The  objection  to  the  use  of  voltameters  is  that  the  conditions 
of  experiment,  such  as  the  strength  of  the  current,  size  of  the 
electrodes,  strength  of  the  solution,  etc.,  may  effect  the  accuracy 
of  the  results. 

If  a  current  flows  through  water  to  which  sulphuric  acid  has 
been  added,  the  water  is  decomposed  and  hydrogen  and  oxygen 
liberated.  These  gases  can  be  collected  in  graduated  tubes  and 
their  volume  measured  from  which  the  Current  strength  can  be 
calculated.  It  is  better  in  practice  to  measure  only  the  hy- 
drogen, for  a  portion  of  the  oxygen  is  condensed  to  ozone, 
and  it  is  also  slightly  soluble  in  the  solution. 

An  ampere  liberates  .1155  cubic  centimeters  of  hydrogen 
per  second,  if  the  volume  be  taken  at  the  barometric  pressure  of 
760  mm.  and  the  temperature  of  o°  C.  The  volume  observed 
must  therefore  be  reduced  to  these  standard  conditions  by  the 
use  of  suitable  formulae.  Then  the  current  in  amperes  =  Volume 
in  C.  C.  ~-  (1155  X  Time  in  seconds). 

Ammeters. — The  following  classification  indicates  a  few  of  the 
more  important  forms  of  instruments  whose  scale  readings  give 
current  strength  directly. 


f  We s ton. 
AMMETERS. 


iAyrton  and  Perry. 
Hartman  and  Braun. 
Evershed's. 
Schuckerfs 
Magnetic  Vane. 

The  Weston  ammeter  is  almost  precisely  similar  in  construc- 
tion to  the  Weston  voltmeter,  shown  by  Fig.  64.  The  movable 
coil,  however,  instead  of  being  connected  in  series  with  a  high 
resistance,  is  joined  in  parallel  with  a  low  resistance.  This 
shunt  in  some  of  the  instruments  consists  of  a  number  of  copper 
wires  wound  in  parallel  about  the  magnet  and  has  about  .002 
ohm  resistance. 


94 


ELECTRICAL  MEASUREMENTS. 


FIG.  76. 


It  is  hardly  necessary  to  say  that  the  portable  standard  form 
of  these  ammeters  are  extremely  reliable  and  accurate  instru- 
ments. 

One  form  of  the  Ayrton  and  Perry  ammeter  is  shown  in 
Fig.  76.  A  short  magnetic  needle  is  placed 
between  the  pole  pieces  of  a  powerful  perm- 
anent magnet  which  controls  its  direction 
and  renders  it  independent  of  the  earth's 
magnetism.  When  a  current  flows  through 
the  solenoid,  it  tends  to  rotate  the  needle 
toward  the  axis  of  the  coil.  This  coil  is  of 
very  low  resistance  and  consists  of  but  few 
turns  of  copper  wire.  By  the  proper  shap- 
ing of  the  pole  pieces,  needle,  and  coil,  the 
angular  deflections  are  made  proportional  to 
the  strength  of  the  current. 
An  ammeter  largely  manufactured  by  Hartman  and  Braun, 
of  Frankfort,  and  used  to  a  considerable  extent  abroad,  is  shown 
in  Fig.  77.  A  very  small  tube,  made  of  soft,  thin  sheet  iron,  is 
attached  to  a  spring  and  lever  arm,  and  placed  near  the  end  of 
an  attracting  solenoid  consisting  of  a  few 
turns  of  stout  copper  wire.  By  correctly 
.shaping  the  tube,  the  deflections  can  be 
made  proportional  to  the  strength  of  current. 
It  is  claimed  in  the  most  recent  instruments, 
that  the  effects  of  residual  magnetism  and 
hysteresis  are  practically  eliminated.  This 
instrument  in  somewhat  simpler  form  is 
known  as  the  Kohlrausch  ammeter. 

The  Evershed  instrument, known  as  the  "Gravity"  ammeter, 
consists  of  a  magnetizing  coil,  placed  with  its  axis  horizontal. 
In  the  older  form  of  these  instruments,  a  small  cylindrical  piece 
of  soft  iron  fixed  to  a  spindle  pivoted  at  its  extremities,  is  placed 
within  a  coil  and  counter-weighted  to  maintain  in  certain  posi- 
tion. When  a  current  flows  through  the  coil,  the  iron  is  rotated 
toward  a  position  between  the  ends  of  two  plates  of  iron  also 
within  the  coil,  but  not  shown  in  the  diagram. 

For  very  heavy  currents,  the  magnetizing  coil  consists  of  a 
massive  tubular  casting  of  copper  divided  by  saw- cuts  to  form 
a  "coil."  V, 

In  the  more  recent  form  of  this  instrument,  two  curved  pieces 
of  iron  are  placed  within  the  coil.  The  outer  is  fixed  and  con- 
centric with  the  inner  one,  which  is  mounted  on  the  counter- 
weighted  spindle.  When  a  current  flows  through  the  coil,  the 


FIG.   77. 


AMMETERS.  95 

movable  piece  of  iron  is  urged  round  towards  the  position  where 
the  two  pieces  would  form  approximately  a  complete  tube  of  iron. 

This  same  construction  is  also  used  for  the  Evershed  volt- 
meters. 

A  possible  source  of  error  in  the  above  described  am- 
meters is  the  retentivity  of  the  iron.  It  is,  therefore,  well  to 
test  the  readings  with  an  increasing  and  decreasing  current. 

In  the  Schuckert  ammeter,  an  index  is  pivoted  in  the  axis  of 
the  magnetizing  coil,  and  carries  a  light  strip  of  soft  iron.  An- 
other strip  is  fixed  with  the  coil.  When  a  current  flows  through 
the  coil,  these  strips  become  magnetized  and  repel  one  another. 
The  controlling  force  is  gravity. 

The  principle  of  the  "  Magnetic  Vane  "  ammeter  is  similar 
to  the  above,  the  motion  of  the  movable  vane  being  opposed  by 
a  spring. 

With  regard  to  the  various  forms  of  ammeters  just  described, 
depending  on  the  magnetic  effect  of  a  coil  on  iron,  it  is  not 
easy  to  say  just  how  reliable  or  unreliable  any  particular  instru- 
ment under  varying  conditions  may  be.  Their  chief  advantage 
is,  that  they  can  be  made  more  sensitive  for  a  certain  portion  of 
the  scale,  that  is,  for  a  given  strength  of  current,  and  that  they 
may  be  employed  for  alternating  as  well  as  .direct  currents. 

Whenever  possible,  however,  the  use  of  a  Weston  ammeter  is 
to  be  recommended,  or,  better  still,  a  standard  Weston  volt- 
meter, across  a  shunt,  for  in  this  case,  by  varying  the  resistance 
of  the  shunt,  the  range  of  measurement  is  unlimited. 

f  Dynamometer. 
I    Current  Balance. 

( ,„          c    i   "Attraction  "  or  Electro-Magnetic  A mmeters. 
rs'   |   P.  D.  and  Shunt. 
[  Calorimetric  Method. 

It  should  be  understood  that  the  methods  and  instruments 
described  for  alternating  currents  are  also  suitable  for  the 
measurements  of  direct  currents. 

The  dynamometer  and  current  balance  might  have  been 
classified  with  ammeters,  since  they  are  current  measuring 
instruments,  but  on  account  of  their  importance  it  is  perhaps 
better  to  treat  them  separately. 

Dynamo  me tcr.-*-r£\&  principle  of  the  electrodynamometer  has 
been  previously  explained,  and  is  shown  in  Fig.  67.  For  the 
measurement  of  current,  the  coils  should  be  of  very  low  resis- 
tance. 

In  the  Siemens  dynamometer,  much  used  for  the  measure- 
ment of  strong  currents,  whether  direct  or  alternating,  one  coil 


96  ELECTRICAL  MEASUREMENTS. 

is  fixed  permanently,  whilst  the  other  coil,  of  one  or  two  turns, 
dipping  with  its  ends  in  mercury  cups,  is  hung  at  right  angles, 
and  controlled  by  a  special  spring  below  a  torsion  head.  When 
a  current  passes,  the  movable  coil  tends  to  turn  parallel  to  the 
fixed  coil,  but  is  prevented  ;  the  torsion  index  being  turned  un- 
til the  twist  on  the  spring  balances  the  torque.  The  angle 
through  which  the  index  has  had  to  be  turned  is  proportional  to 
the  square  of  the  current  strength. 

The  axis  of  the  movable  coil  should  be  in  the  line  of  the 
magnetic  meridian,  and  the  coils  should  be  accurately  perpen- 
dicular to  each  other. 

Where  current  strength  is  determined  by  the  deflections  of  a 
dynamometer,  the  mean  current  strength  of  an  alternating  cur- 
rent is  TV  of  the  strength  of  the  continuous  current,  which 
would  give  the  same  deflection. 

Current  Balance. — The  principle  of  the  Thomson  current 
balance  is  indicated  by  Fig.  78.  There  are  four  fixed  coils, 

A,  B,  c,  D,  between  which  is  suspended, 

J~^  s-^^2    by  a  flexible  metal   ligament  of  fine 

^h^  i  (     r2^      wires,  at  the  ends  of  a  light  beam,  a 

pair  of  movable  coils,  E  and  F.  The 
current  flows  in  such  directions  through 
the  whole  six,  that  the  beam  tends  to 
rise  at  F,  and  sink  at  E.  The  beam 
carries  a  small  pan  at  the  end  F,  and  a 
FIG.  78.  light  arm  along  which  a  sliding  weight 

can  be  moved  to  balance  the  torque 

due  to  the  current.  The  current  is  proportional  to  the  square- 
root  of  this  torque,  the  force  being  proportional  to  the  product 
of  the  current  in  the  fixed  and  movable  coils,  as  in  all  electro- 
dynamometers.  The  current  balance  is  in  fact  a  current  weigh- 
ing dynamometer. 

A  complete  range  of  these  instruments  has  been  designed, 
reading  from  .01  ampere  to  2,500  amperes. 

The  Thomson  balance  forms  a  most  reliable  standard  for  the 
measurement  of  current  and  the  calibration  of  other  instru- 
ments. 

When  these  instruments  are  made  so  as  to  measure  alternat- 
ing as  well  as  continuous  currents,  the  current  is  carried  by  a 
twisted  rope  of  copper  wires,  each  of  which  is  insulated.  The 
object  of  this  arrangement  is  to  prevent  inductive  action. 

*'  Attraction  "  or  Electro-Magnetic  Ammeters. — Alternating  cur- 
rents may  be  measured  with  more  or  less  accuracy  by  the  vari- 
ous forms  of  these  ammeters,  such  as  the  Evershed,  Schuckert, 
etc.,  previously  described. 


AMMETERS.  97 

When  such  an  electromagnetic  ammeter  is  employed  for  the 
measurement  of  alternating  currents,  the  general  tendency  is 
for  its  readings  to  be  lower  than  the  correct  value,  if  it  is  calib- 
rated to  be  correct  for  direct  currents,  chiefly  on  account  of  the 
«ddy  currents  which  are  set  up  in  the  framework  and  metal 
parts  of  the  instrument.  It  is  found  that  the  Evershed  am- 
meters indicate  about  two  per  cent,  lower  than  the  true  value  of 
such  an  alternating  current.  This  error,  however,  is  corrected 
by  permanently  shunting  the  main  ammeter  coil  by  a  smaller 
coil  of  copper  wire  which  is  overwound  with  thin  iron  wire,  in 
order  to  raise  its  self-induction  to  the  desired  value. 

If  there  be  any  hysteresis  or  retentivity  in  the  iron  used  in 
this  class  of  ammeters,  the  error  caused  by  it  may  be  considerable. 

P.  D,  and  Shunt. — An  alternating  current  may  be  conveniently 
and  accurately  determined,  if  the  potential  difference  across  a 
shunt  of  known  resistance  be  measured  by  means  of  a  Weston 
alternating  current  voltmeter  or  some  form  of  electrometer. 
Since  these  instruments  are  not  very  sensitive  for  small  poten- 
tial differences,  and  the  resistance  of  the  shunt  must  necessarily 
be  low,  the  above  applies  especially  to  strong  currents. 

Calorimetric  Method. — The  heat  units,  or  calories  developed  by 
a  current  in  a  given  time,  is  equal  to  .24  C2  R  T,  where  C  is  the 
current  in  amperes,  R  the  resistance,  and  T  the  time  in  seconds. 
Therefore,  if  this  amount  of  heat  be  determined  by  means  of  a 
calorimeter,  the  current  strength  can  be  calculated.  The 
method,  however,  is  not  a  very  practical  one. 

If  the  expansion  of  a  wire  were  used  to  indicate  the  current, 
as  in  the  case  of  the  Cardew  voltmeter,  the  resistance  would  be 
too  high  to  introduce  into  the  circuit. 

Very  High  Currents 

and 
Very  Low  Currents. 

It  has  been  stated  that  the  measurement  of  potential  differ- 
ence across  a  shunt  of  known  resistance  is  a  universal  method 
for  the  measurement  of  current,  and  it  is  especially  desirable 
for  the  determination  of  very  strong  or  very  weak  currents. 

Suppose  the  standard  form  of  Weston  voltmeter  be  employed, 
with  which  readings  can  be  made  from  ^^  volt  to  150  volts,  and 
that  a  shunt  of  .0001  ohm  be  used.  Then  the  range  of  measure- 
ment would  be  from  33  amperes  to  1,500,000  amperes. 

Now,  the  resistance  of  such  a  current  could  be  very  accurately 
measured  by  means  of  the  double  bridge,  the  best  plan  being  to 
determine  the  resistance  between  two  marks  on  a  heavy  bar  of 
copper.  The  leads  from  the  voltmeter  should  then  be  connected 


98  ELECTRICAL  MEASUREMENTS. 

to  knife  edges  resting  upon  these  marks.  Since  the  resistance 
of  the  Weston  voltmeter,  even  when  the  low  reading  scale  is 
used,  is  about  500  ohms,  the  resistance  of  the  leads  and  contacts 
would  be  entirely  negligible  compared  to  it. 

A  mistake  probably  often  made  when  very  heavy  currents  are 
to  be  measured,  is  that  of  shunting  a  low  reading  ammeter. 
Here  the  case  is  entirely  different,  for  then  the  contact  resis- 
tances are  added  on  to  the  low  resistance  of  the  ammeter  and 
may  produce  a  considerable  error,  even  though  the  shunt  has- 
been  most  accurately  adjusted. 

Since  a  sensitive  high  resistance  galvanometer  will  indicate  a. 
micro-volt,  if  the  galvanometer  be  shunted  across  one  ohm,  it  is- 
then  possible  to  measure  current  to  one  millionth  of  an  ampere. 

Calibration  of  Ammeters. — The  best  method  of  calibrating  an 
ammeter  is  to  compare  the  readings  with  those  of  a  standard 
Weston  voltmeter  shunted  across  a  known  resistance.  The  ar- 
rangement is  shown  in  Fig.  79,  R  being  the  resistance,  and  r  an 
adjustable  resistance  to  vary  the  current. 

The  correct  strength  of  current  is,  of  course,  given  by 
the  voltmeter  reading  divided  by 

the  resistance  of  the  shunt     In  place          Illlllll        \AV\A/ 
of    the  voltmeter,   the  potentiometer 
can  be  used,  according  to  the  method 
given  for  calibrating  a  voltmeter. 

vSince  the  voltmeter  may  be  com- 
pared to  the  Clark  cell  by  means  of 
the  potentiometer,  and  the  shunt  resis- 
tance to  the  standard  ohm,  the  stand- 
dards  of  E.  M.  F.  and  resistance  become  .  FIG.  79. 

also  the  standards  for  current. 

By  means  of  the  Thomson  balance,  an  ammeter  can  be  very 
accurately  calibrated. 

The  ammeter  can  also  be  checked  by  comparison  with  the 
voltmeter. 

When  it  is  desired  to  compare  a  low  reading  ammeter  that 
has  been  calibrated  with  a  high  read- 
B       ^y  mg  ammeter,  the  arrangement  shown, 

vVW      v  in  Fig.  80  can   be   employed.      If   the 

resistance  of  the  shunt  r  is  equal  to  ^ 
of  the  resistance  of  Ammeter  i  4-  Rr 
then  ammeter  i  will  only  receive  .01  of 
the  entire  current  that  flows  through, 
FIG.  80.  ammeter  2.  By  this  means  an  am- 

meter only  reading  to  15  amperes  could 
be  compared  with  one  reading  to  1,500  amperes. 


AMMETERS.  99 

Absolute  Determination  of  Current. — Current  strength  can  be 
measured  in  absolute  units  from  the  deflections  of  a  tangent 
galvanometer,  if  its  radius,  number  of  turns,  and  strength  of 
surrounding  field  be  known.  The  equation  is  : 

C=  ——  X  &  X  tan  a  , 

2  W  7T 

where  r  is  the  radius  of  the  galvanometer  coils  in  centimetres, 
n  the  number  of  turns,  H  the  strength  of  field,  and  a.  the  de- 
flection. 

Considerable  care  should  be  used  in  this  determination,  if 
accurate  results  are  desired. 

This  method  is  interesting  on  account  of  its  employment  in 
the  determination  of  the  value  of  the  standard  ohm,  and  also- 
forms  an  additional  check  on  the  other  methods  of  current 
measurement. 


CHAPTER  XVIII. 


r  j  Weston's. 

ENERGY.]  Wattmeter.  \  Siemens'. 

[_  Voltmeter  and  Ammeter. 

The  amount  of  electrical  power  consumed  by  lamps,  motors, 
•etc.,  can  be  directly  measured  by  means  of  instruments  known 
as  voltmeters. 

The  unit  of  electrical  energy  is  the  watt,  or  kilowatt  (=  1,000 
watts),  and  a  horse-power  is  equivalent  to  about  746  watts. 

Most  of  these  wattmeters  are  modifications  of  Weber's  dynamo- 
meter, in  which  a  fixed  coil  produces  a  field,  and  tends  to  turn 
a  movable  coil.     One  of  the  best  known  wattmeters  is  Siemens' 
dynamometer,  in  which  one  coil  is  wound  with  fine  wire  and  is 
put  in  shunt  to  the  part  of  the  circuit  in  which  the  power  is  to 
be  measured,  and  a  thick  wire  coil  which  is  joined  in  series. 
The  force  is  then  proportional  to  the  product  of  the  currents  in 
the  two  coils,  that  is,  to  the  product  of  the  potential  difference 
and  current,  or  to  the  power.     In  the  Weston  wattmeter,  the 
motion  of  the  movable  coil  is  opposed  by  a  spring  in  a  manner 
similar  to  that  used  in  the  voltmeter  and  ammeter. 

The  resistance  of  the  pressure  or  shunt  coil  should  be  as  high 
as  possible,  since  the  current  that  it  takes  also  passes  through 
the  series  coil,  and  may  thus  cause  a  considerable  error.    As  the 
pressure  coil  generally  takes  more  power  than  the  current  coil, 
it  is  best  to  put  it  in  shunt  to  the  current  coil  in  addition  to  the 

lamp  or  other  device   across 
which  the  power  is  to  be  deter- 
mined.   Some  wattmeters  are 
compensated  for  this  error. 

Electrical   energy  can  be 
very  readily    determined   by 
means  of  the  voltmeter  and 
ammeter.      The  voltmeter  is 
_______  used  in  shunt  and  the  ammeter 

FIG.  81.  in   series  (Fig.  81),   and    the 

power  is  then  obtained  by  multiplying  the  potential  difference 

100 


ENERGY.  lor 

indicated  by  the  voltmeter  by  the  reading  of  the  ammeter.  If 
a  Weston  standard  voltmeter  be  employed,  the  error  caused  by 
the  current  taken  by  the  voltmeter  is  very  small.  This  error 
may  be  still  further  reduced  by  placing  the  voltmeter  also  in 
shunt  to  the  ammeter. 

(  Voltameter.     (Edison  Meter.) 
QUANTITY.  \  "Meters." 

(  Ballistic  Galvanometer. 

The  amount  of  electrolytic  action  in  any  voltameter  is  pro- 
portional to  the  strength  of  current  and  the  time  ;  that  is  to  say, 
it  is  proportional  to  the  quantity  of  electricity.  The  unit  of 
measurement  is  the  ampere  second  or  coulomb.  The  practical 
unit  is  the  ampere  hour. 

The  voltameter  generally  used  in  practice  is  the  Edison 
"  chemical  "  meter.  It  consists  of  two  jars  of  zinc  sulphate  with 
zinc  electrodes  so  connected  across  a  shunt  that  they  receive, 
say,  J^VTT  °f  tne  entire  current.  The  resistance  of  an  electrolyte 
decreases  with  a  rise  in  temperature.  To  compensate  for  this 
error,  copper  wires  are  joined  in  series  with  the  cells.  Two 
cells  are  used  for  greater  accuracy,  the  amount  the  electrodes 
lose  in  weight  in  each  being  determined.  These  two  results 
should,  of  course,  check  each  other.  The  coulomb  deposits 
0.33696  milligramme  of  zinc,  and  the  ampere- 
hour  1,213  milligrammes.  The  arrangement 
of  the  Edison  meter  is  shown  in  Fig.  82. 

It  is  extremely  difficult  to  measure  satis- 
factorily electrical  quantity  on  a  commercial 
scale.  A  number  of  instruments  have  been 
devised  for  this  purpose,  and  they  are  known 
under  the  general  name  of  "  meters."  Prob- 
ably one  of  the  best  of  these  meters  is  the  Thomson-Houston 
recording  wattmeter.  It  consists  essentially  of  two  thick  wire 
coils  placed  in  series  in  the  circuit,  and  a  thin  wire  coil  placed 
in  shunt  around  the  circuit  whose  power  is  to  be  measured.  The 
shunt  coil  is  mounted  on  an  axle  carrying  a  copper  disk  moving 
between  the  poles  of  permanent  magnets.  Under  these  condi- 
tions, the  rate  of  rotation  produced  in  the  movable  coil  is  pro- 
portional to  the  energy  consumed  in  the  main  circuit.  The 
number  of  revolutions  is  recorded  by  clockwork  and  the  instru- 
ment is  graduated  to  indicate  watt-hours,  etc. 

In  the  Forbes'  meter,  the  current  passes  through  a  number  of 
fine  wires  placed  in  parallel.  These  wires  becoming  heated, 
produce  a  rising  current  of  warm  air,  and  this  rotates  a  spindle 
carrying  mica  vanes. 


102  ELECTRICAL  MEASUREMENTS. 

The  Ferranti  meter  consists  of  a  vessel  containing  mercury, 
above  which  is  placed  a  solenoid.  The  current  is  led  to  the 
mercury  at  the  centre  of  the  vessel  and  leaves  it  at  the  cir- 
cumference, then  passing  through  the  magnetizing  solenoid, 
the  mercury  is  urged  to  move  in  a  direction  at  right  angles  to 
that  in  which  the  current  is  flowing  through  it,  and  also  at  right 
angles  to  the  lines  of  force  of  the  field.  This,  of  course,  pro- 
duces rotation.  The  amount  of  rotation  is  measured  by  means 
of  a  float  geared  to  the  proper  indicating  device,. 

The  Aron  meter  consists  of  two  clocks  geared  differently. 
The  pendulum  of  one  clock  carries  a  permanent  magnet.  Be- 
neath this  is  placed  a  solenoid,  through  which  flows  the  main 
current.  When  both  pendulums  oscillate  at  the  same  rate,  no 
movement  of  the  indicating  pointers  takes  place,  but  they  begin 
to  indicate  if  one  of  the  pendulums  is  accelerated.  This  accel- 
eration is  proportional  to  the  strength  of  the  current  flowing 
through  the  solenoid.  They  can  be  adjusted  to  indicate  ampere- 
hours. 

In  order  to  make  this  or  any  similar  meter  show  the  energy 
consumed,  or  watt-hours,  it  is  necessary  to  multiply  the  ampere- 
hours  by  the  pressure  at  which  the  current  is  supplied.  There- 
fore the  accuracy  of  the  result  depends  upon  the  constancy  of 
the  pressure  as  well  as  the  accuracy  of  the  instrument. 

The  deflections  of  a  ballistic  galvanometer  are  proportional 
to  the  quantity  of  electricity  passing  through  the  galvanometer, 
if  the  discharge  occupy  a  very  short  time  compared  to  the  time 
of  vibration  of  the  galvanometer  needle.  The  application  of 
this  fact,  however,  is  in  the  absolute  determination  of  capacity 
and  inductance. 


CHAPTER   XIX. 
CAPACITY. 


DEFLECTION 


Direct  Deflection* 
Direct  C 


rr         .T  (  Bridge  Method. 

ZERO  METHODS.,  -j  Pote*tiometer  Method  (Mixtures.)* 

ABSOLUTE  DETERMINATION  (Ballistic  Galvanometer.) 

Electrostatic  capacity  may  be  defined  as  the  ratio  of  the  quan- 
tity of  any  electrical  charge  to  the  E.  M.  F.  producing  that  charge, 

or  F  =  Sr,     Scientifically  speaking,  it  is  the  ratio  of  dielectric 

strain  to  dielectric  stress,  the  term  "  quantity  "  of  electricity  be- 
ing used  only  as  a  matter  of  convenience.  The  unit  of  capacity, 
or  the  farad  (^),  is  such  a  capacity  that  the  unit  quantity,  one 
coulomb,  is  obtained  under  the  pressure  of  one  volt.  This  ca- 
pacity is  far  too  large  tor  ordinary  measurements,  so  the  prac- 
tical unit  employed  is  a  millionth  of  this,  or  the  micro-farad. 

The  accurate  determination  of  capacity  in  many  cases  is  im- 
possible, since  most  condensers,  to  a  certain  extent  at  least,  and 
practically  all  cables  exhibit  the  phenomena  of  absorption  and 
residual  charge.  Therefore,  when  the  capacity  is  stated,  all  the 
conditions  of  measurements  should  be  given. 

Direct  Deflection. — In  this  method,  a  standard  condenser,  F,  is 
charged  by  a  battery,  B,  Fig.  83,  and  then  dicharged  through 
a  high  resistance  galvanometer,  and  the  de- 
flection d  observed.  The  unknown  condenser, 
F2,  is  then  substituted,  and  the  deflection  dz 
noted.  Then  F!  :  F2  :  :  ^  :  4- 

Some  uniform  time  of  charge,  such  as  five 
seconds,  should  be  adopted.     Several  observa- 
tions should  be  taken  in  each  case,  and  the          F*G.  83. 
mean  used  in  the  calculation.     The  method  is  suitable  and  con- 
venient where  only  approximate  results  are  desired, 


104  ELECTRICAL  MEASUREMENTS. 

The  absorption  of  various  condensers  may  be  studied  by 
this  method  by  observing  the  deflection  after  charging  for  dif- 
ferent lengths  of  time,  such  as  i  second,  30  seconds,  i  minute, 
etc.  The  residual  charge  can  be  determined  by  discharging,  in- 
sulating for  one  minute,  and  discharging  again,  insulating  for 
another  minute,  etc. 

It  is  important  in  the  above  method  that  there  be  no  self-induc- 
tion in  any  portion  of  the  circuit,  or  in  the  galvanometer  shuntr 
if  it  be  employed,  for,  of  course,  this  would  change  the  value 
of  the  deflections  and  thus  cause  an  additional  error  in  the 
measurement. 

Divided  Charge. — The  connections  for  this  method  are  shown 
in  Fig.  84.  The  standard  condenser,  F,  is  charged  by  closing 
the  battery  key,  k.  It  is  then  discharged,  and 
the  deflection,  d,  noted.  It  is  again  charged, 
the  key  k  is  opened  and  the  key  K  depressed 
for  a  few  seconds,  by  this  means  allowing 
the  charge  to  divide  between  the  two  con- 
densers, F2,  being  the  unknown  condenser  or 
eable.  The  standard  condenser  is  then  once 
more  discharged.  Call  this  deflection  4,  then 
^i  —  4,  f°r  the  quantity  of  charge  in  each  con- 
denser is  proportional  to  the  capacity.  This  method  is  said  to 
be  very  accurate  for  the  measurement  ot  the  capacity  of  long 
cables. 

Loss  of  Charge — Discharge. — The  capacity  of  a  condenser  can 
be  calculated  from  the  formula 

T 


2.303  R  (log  4  —  log  4) 

when  d  is  the  discharge  deflection  obtained  immediately  after 
charging,  4  the  deflection  after  charging,  and  then  insulating 
for  T  seconds,  R  the  resistance  between  the  poles  of  the  con- 
denser (if  this  be  expressed  in  megohms,  the  capacity  will  be 
obtained  in  micro -farads),  and  2.303  the  modulus  to  convert  the 
ordinary  or  Brigg's  logarithms  to  natural  logarithms.  The  con- 
nections are  the  same  as  Fig.  83.  If  a  mica  condenser  be  used, 
a  resistance  of  several  megohms  may  be  placed  between  the 
poles.  To  measure  the  capacity  of  cables  by^this  method,  the 
insulation  must  be  determined  and  this  value  substituted  for  R. 
Since  the  insulation  is  such  a  variable  quantity,  the  above 
method  is  only  very  approximate. 

Deflection.— K  modification  of  the  method   just   described   is 
shown  in  Fig.  85. 


CAPACITY. 


105 


The  steady  deflection  is  first  observed  with  the  key  closed, 
d\  it  is  then  noted  after  T  seconds  4,  and  the 
capacity  calulated  from  the  formula  given 
above.  The  resistance,  R,  should  be  great 
enough,  several  megohms,  so  that  the  charge 
will  not  be  lost  too  rapidly.  If  the  resistance 
of  the  condenser  be  low  or  if  a  cable  is  used, 
and  if  this  resistance  be  callled  r,  then  the 
value  of  the  resistance  to  be  used  in  the  above  equation 

Rr 


Bridge  Method.  —  Zero  methods  have  the  advantage  that  the 

errors  due  to  reading  the  galvanometer  deflections  are  avoided, 

and  that  the  effects  due  to  induction  may  be  partially,  if  not 

entirely,  eliminated. 
The  Bridge  method  is  applicable  to  ordinary  condenser  work 

and  to  short  lengths  of  cable,  but  is  not  suitable  for  great 
lengths  of  cable,  on  account  of  the  influence  of 
inductive  retardation.  The  connections  for  the 
measurement  are  shown  in  Fig.  86.  The 
method  is  very  similar  to  the  Wheatstone 
bridge.  When  the  resistances  Rl  Rz,  which 
should  be  high,  are  so  adjusted  that  there  is- 
no  deflection  of  the  galvanometer  on  making 
contact  at  a  or  b,  then  Rl  :  R»  :  :  F*  :  F^.  That 

is,  the  capacities  are  inversely  proportional  to  the  resistances, 

During  the  adjustment  of  R^  R.,,  contact  should  be  made  at  the 

point  b,  in  order  that  the  condensers  are  kept  discharged.     If 

the  insulation  of  the  condensers  be  not    good,  of   course,  an 

error  may  be  caused  by  the  current  flowing  through  the  con- 

densers. 

Method  of  Mixtures  (Thomson's  Method).  —  This  method  may 

be  considered   the   standard  for  cable  work,  and  is  also  very- 

suitable  when   the   most  accurate  comparison 

of    condensers    is   desired.     The   method   de- 

pends  on  the  principle  that   the   "quantity" 

of  electricity  in  a  condenser  is  equal  to  its  ca- 

pacity,  multiplied  by  the   p.  D.  of  the  charge, 

or  Q  =  F  E.      If,  then,  two  condensers  Fl  Fz 

have  the  same  charge,  Q  =  Fl  E^  =  F2  E%,  or 

Fv  :  F.2  :  ;  Ez  :  E±.     In  this  method  the  ratios  of 

E^  Ez  are  the  same  as  the  resistances  R±  R*,  ; 

hence,  F1  :  Fz  :  Rz  :  Rr      The  arrangement  for  this  measure- 

ment is  shown  by  the  diagram,  Fig.  87. 


FIG.  87. 


io6  ELECTRICAL  MEASUREMENTS. 

The  rheostat  ^  Rz  should  be  of  high  resistance.  It  is  con- 
venient to  use  in  place  of  them  one  of  the  "  potentiometers  "  or 
slide  coil  bridges  previously  described.  It  is  best  to  employ  a 
special  key,  known  as  the  Lambert  capacity  key,  indicated  in  the 
diagram  by  L. 

The  manipulation  is  as  follows  :  Contact  is  made  at  the 
points  ab,  and  the  condensers  are  thus  charged  across  Rv  and 
j?2.  Contact  is  then  made  at  the  points  c  d,  and  by  this  means 
the  charges  of  the  condensers  are  allowed  to  mix.  Finally, 
contact  is  made  at  e,  and  the  galvanometer,  being  thus  placed 
in  circuit  with  the  condensers,  is  deflected,  if  the  charges  are 
unequal.  The  adjustment  of  Rl  Rz  is  repeated  until  the  gal- 
vanometer shows  no  deflection.  Some  standard  time  of  charg- 
ing should  be  employed,  say,  ten  seconds,  and  the  charges 
should  be  allowed  to  mix  ten  seconds.  For  long  cables,  a  five 
minute  charge  is  recommended  and  a  time  of  mixture  of  ten 
.seconds. 

The  values  of  F^  F2  should  not  be  very  unequal  —  that  is,  F± 
should  not  be  much  less  than  \  of  F&  for  if  the  capacities  are 
very  different,  the  potential  of  one  charge  may  be  so  much 
higher  than  that  of  the  other  that  an  error  may  be  caused  by 
.absorption. 

Absolute  Determination.  —  The  "  quantity  "  of  electricity  which 
-discharged  through  a  ballistic  galvanometer  will  produce  a 
given  deflection  is  expressed  by  the  equation 


In  the  above  equation  --  *  is  the  "  constant  "  of  the  galvanometer, 
EI 

that  is,  if  a  potential  difference  E±  be  used  through  a  resistance 
R,  a  steady  deflection  d±  is  obtained.  4  is  the  throw  of  the 
galvanometer  produced  by  the  quantity  Q,  T  the  time  in  seconds 
of  a  complete  or  double  vibration  of  the  galvanometer  on  open 
circuit,  and  /  is  the  logarithmic  decrement. 

If  a  condenser  of  capacity  F  be  charged  by  a  potential  differ- 
ence -#2  ,  then  since 


consequently 

4  T((I  +       E, 

V 


2  TT 


In  a  ballistic  galvanometer,  the  time  of  vibration  of  the  mov- 
ing system  should  be  slow,  the  moment  of  inertia  large,  and  the 


CAPACITY. 


107 


decrement  or  damping  but  slight.  These  conditions  are  fulfilled 
by  several  forms  of  galvanometer.  One  in  which  bell  magnets 
are  employed,  shown  in  Fig.  7,  and  also  the  special  forms  of  the 
D'Arsonval  and  the  Ayrton  and  Mather  galvanometer  previ- 
ously described.  Either  of  the  two  latter  galvanometers  is. 
much  to  be  preferred  for  practical  work  over  the  first  form,  in 
which  the  magnetic  system  is  movable. 

To  observe  the  time  of  vibration  T,  the  galvanometer  is  given 
a  vibration  of  200  to  300  scale  divisions  and  time  of,  say,  10  or 
20  vibrations  determined,  the  mean  of  several  sets  of  observa- 
tion should  be  taken.  If  a  galvanometer  with  movable  magnetic 
system  is  employed,  the  deflections  are  con- 
trolled by  means  of  a  "  check  coil,"  that  is  a 
solenoid  in  series  with  cell  placed  near  the 
galvanometer,  Fig.  88.  If  the  D'Arsonval 
form  of  galvanometer  is  used,  a  cell  and  key 
may  be  placed  in  series  with  the  galvanometer,  or  the  galvano- 
meter may  be  brought  to  rest  by  short  circuiting. 

The  decrement  is  the  ratio  of  the  amplitude  of  any  vibration 
to  that  of  the  next  succeeding  vibration.  To  obtain  this,  the 
tenth  vibration  after  the  first  should  be  observed.  Suppose  this 
ratio  is  1 140  ;  then  the  decrement  equals  1.04.  If  the  decrement 
is  small,  such  as  the  above  example,  then  it  is  sufficiently  ac- 
curate to  call  the  factor  f  i  4--1  equal  to  1.02.  Actually  A  is 


FIG.   88. 


f  i  -f"  -)  equal 


equal  to  the  log.  of  the  decrement  X  2.303. 

To  determine  the  "  constant "  of  the  galvanometer,  the  deflec- 
tion ^  is  observed  when  a  constant  cell,  such  as  a  Daniell  cell, 
or  preferably  a  storage  cell,  is  used.  The  galvanometer  may  be 
shunted,  a  high  resistance  placed  in  series  with,  or  better  still, 
the  cell  can  be  shunted.  This  last  arrangement  is  shown  in 
Fig.  89.  In  this  case  R  is  the  resistance  of 
the  galvanometer  and  El  is  equal  to  E  x  .004. 
Then  condenser  F  is  charged  by  the  same 
cell,  shunted  if  need  be,  and  the  deflection 
dz  observed.  The  arrangement  is  shown  by 
Fig.  90.  Here  £2  is  equal  to  E  x  .700. 
Thus  the  E.  M.  F.  of  the  cell  need  not  be 
known,  since  it  cancels  the  equation  given  above. 

This  method  of  measuring  capacity  is  of 
considerable  importance,  for  by  it  a  standard 
condenser  may  be  accurately  calibrated.  Of 
course,  after  the  capacity  of  a  standard  is 
once  accurately  known,  other  standard  con- 
densers can  be  compared  to  it. 


FIG.  89. 


CHAPTER  XX. 


INDUCTANCE. 


BRIDGE  METHOD  (Maxwell's.) 
COMPARISON  WITH  STANDARD. 
SECOHMMETER         j  With  Standard. 

METHOD.  \  Without 
CONDENSER  \  Deflection. 

METHOD.    {  Zero. 
CALCULATION. 
[IMPEDANCE.] 

By  the  term  "  inductance  "  is  meant  the  coefficient  of  self-in- 
duction. 

When  a  current  flows  through  a  circuit,  a  magnetic  field  is 
established  about  the  conductor  carrying  the  current. 

If  the  strength  of  the  current  rises,  the  strength  of  the  field 
also  varies.  This  has  the  effect  of  producing  or  withdrawing 
"lines  of  force,"  and  if  these  cut  adjacent  wires  in  the  circuitr 
an  E.  M.  F.  is  developed  in  a  direction  opposite  to  that  in  which 
the  current  is  flowing. 

The  unit  of  the  inductance  (L)  is  the  henry  or  such  an  induct- 
ance that  if  the  current  varies  one  ampere  per  second,  a  counter 
E.  M.  F.  of  one  volt  is  developed.  From  a  consideration  of  the 
absolute  system  of  units  and  dimensional  formulae,  this  has  also 
been  known  as  the  "  secohm  "  or  "quadrant." 

This  coefficient  may  be  determined  by  several  methods. 
Bridge  Method. — This  method   requires    a   ballistic  galvano- 
meter.    The  coil  s,  whose  inductance  is  required,  is  placed  in 
the  arm,  c  d,  of  a  P.  O.  bridge,  Fig.  91.     The 
bridge  coils,  A,  B,  are  made  equal  to  each  other, 
and  as  nearly  equal  to  s  as  possible.    An  extra 
rheostat,   R2,   is  multiplied   with    RX;   by   this 
means,  an  exceedingly  fine  adjustment  can  be 
obtained.    All  the  resistances,  except  s,  should 
FIG.  91.  foe  non-inductive. 

The  resistance  in  the  arm  e  c  is  adjusted  until  on  closing,  first 
the  battery  key  and  then  the  galvanometer  key,  no  deflection  is 

108 


INDUCTANCE.  109 

observed.  The  galvanometer  key  is  then  first  closed,  and  after- 
wards the  battery  key  and  the  throw  of  the  galvanometer,  dz 
caused  by  the  inductance  of  s  obtained.  The  resistance  in  the 
arm  e  c  is  changed  a  small  amount  by  altering  the  resistance  in  R8. 
Call  this  change  of  resistance  in  the  arm  e  e  equal  to  r.  The  bat- 
tery key  is  then  closed,  and  the  steady  deflection,  dl  obtained  on 
closing  the  galvanometer  key  observed.  The  inductance  is  then 
obtained  by  the  equation 

L  =  T-Ji   X  Tic  X   ('  +  - 

where  T  is  the  time  in  seconds  of  a  complete  or  double  vibra- 
tion of  the  galvanometer,  and  A  the  "  logarithmic  decrement." 
These  latter  constants  should  be  determined  in  a  similar  man- 
ner to  that  given  for  the  absolute  measurement  of  capacity. 

The  complete  equation  requires  in  place  of  —  the  expression 

2  sin.  /2 — 2^  kut  since  the  angle  corresponding  to  dz  is  usually 
tan.  </! 

small,  the  deflections  as  directly  read  off  by  means  of  a  lamp 
and  scale,  or  telescope  and  scale,  give  the  result  with  sufficient 
accuracy  for  ordinary  measurements. 

The  current,  instead  of  being  broken  or  made,  may  be  re- 
versed. In  that  case  the  value  of  dz  is  doubled,  and  by  this 
means  a  more  accurate  reading  obtained. 

Comparison  with  Standard. — If  a  coil  (s^  has  been  standardized 
by  the  above  method,  then  another  inductance  (s2)  may  be  com- 
pared to  it  without  the  use  of  a  ballistic 
galvanometer.  The  arrangement  is  shown 
in  Fig.  92. 

The  resistances  B  and  R2  are  given  some 
constant  value,  such  as  1,000  ohms  each,  and 
are  kept  fixed.  Then  by  the  proper  mani- 
pulation, A  and  RJ  may  be  so  adjusted  that  no 
deflection  is  obtained  either  for  permanent  currents  or  induction. 
When  this  is  the  case,  SA  :  s8  :  :  A  :  B. 

Secohmmeter  Method. — If  a  "  secohmmeter  "  or  automatic  in- 
terrupter and  commutator  be  employed  in  the  battery  circuit, 
then  the  effect  due  to  induction  will  be  a  steady  deflection  in 
place  of  a  throw. 

The  connections  are  the  same  as  those  shown  in  Fig.  91.  The 
resistance  of  A  should  be  made  equal  to  B,  and  the  resistance  of 
the  arm  e  c  adjusted  to  no  deflection  for  steady  currents.  The 
current  is  then  interrupted  by  means  of  the  secohmmeter,  and 
the  resistance  of  the  arm  e  c  changed  by  such  an  amount,  r,  that 


no 


ELECTRICAL  MEASUREMENTS. 


no  deflection  is  observed. 


Then,  L  =  ~,  where  P  is  the  number 

of  interruptions  of  the  current  per  second. 

Any  ordinary  sensitive  galvanometer  will,  of  course,  answer 
for  this  method. 

Adjustable  standards  of  inductance  are  now  made  in  the  form 
of  boxes  of  coils  of  different  values,  and  also  two  coils  in  series 
that  may  be  placed  at  different  angles  to  each  other,  and  the 
inductance  in  milli-henrys  read  off  by  means  of  a 
pointer  and  scale  (Fig.  93).   When  these  standards 
are  at  hand,  the  unknown  inductance,  s.2 ,  is  placed 
in  one  arm  of  a  Wheatstone  bridge,  the  standards, 
Si ,  in  the  other,  and  A  is  made  equal  to  B.     The 
connections  are  indicated  by  Fig.  92.     Then  %  or 
FIG.  93.         Rg  an(j  Si  are  so  a(jjusted  that  no  deflection  is  ob- 
tained for  either  permanent  or  interrupted  currents.    When  this 
adjustment  is  obtained,  s1  =  s, . 

Condenser  Method. — Inductance  may  also  be  compared  to  a 
capacity  by  the  following  method.  The  coil  or  electro-magnet, 
s,  whose  inductance  is  required,  is  joined  in 
one  arm  of  a  Wheatstone  Bridge,  Fig.  94. 
In  series  with  s  is  a  resistance,  r± ,  call  the 
resistance  of  s  equal  tor.,.  Adjustment  is 
made  so  that  no  deflection  is  obtained  with 
permanent  currents.  The  galvanometer  key 
is  then  closed  and  afterwards  the  battery 
key  and  the  throw  of  the  galvanometer  ^  ob- 
served. The  coil  s  is  then  removed  and  a  shunted  condenser,  F,  is 
substituted  in  the  arm  d  c.  Balance  for  steady  currents  is  again 
obtained,  and  the  throw  of  the  galvanometer  on  closing  the 
battery  key  observed.  Call  this  deflection  d, .  Then  if  the  ad- 
justments have  been  so  made  that  rv  -f-  rz  =  rs  -f-  r± , 


FIG.  94. 


A  modification  of  the  above  method  is  shown  in  Fig.  95.  s  is 
the  inductance  to  be  measured  and  F  a  condenser  shunted  by  a 
resistance,  R.  A  balance  for  permanent  currents  should  be  ob- 
tained, and  then  the  deflection  4  ,  on  making 
the  circuit,  with  the  key  /  open,  observed. 
Afterwards  the  deflection  on*  making  circuit 
with  the  key  /closed,  dz  is  obtained.  Then, 

L  —  F  R*       ^ 
—  ' 


FIG  95 


If  the  adjustments  are  so  made  that  there  is  no 


IMPEDANCE. 


in 


deflection  in  either  case,  L  =•  F  JF.  Or  deflections  may  be  ob- 
tained in  opposite  directions,  and  the  value  of  F  corresponding 
to  no  deflection  interpolated. 

Calculation. — The  inductance  of  coils  of  known  dimensions  can 
be  approximately  calculated  in  some  cases.  Thus,  in  the  case 
of  a  long  uniform  solenoid  of  length  /  centimetres,  containing 
n  turns  of  wire,  the  average  radius  of  the  turns  being  r, 

/==  4  ****** 

/ 
(approximately).  t 

Impedance. — Impedance   is  the  opposition   to   the   flow  of  an 
alternating  current.     The  reactance  is  equal  to  the  inductance, 
Z,  multiplied  by  the  period  of  alternation.    The  relation  of  these 
quantities  to  resistance  is  shown  by  Fig.  96.     Thus, 
Impedance  =  y' J&  -f-/Z8, 


FIG.  96. 

and  therefore  the  average  value  of  the  current  is  given  by  the 
equation 


If  there  be  also  capacity  in  an  alternating  current  circuit,  a 
reactance  is  produced  in  a  direction  opposite  to  that  given  by 


inductance.     It  may  be  indicated  by  — 


and  the  resultant 


reactance  would  therefore  be  equal  to/  L  —  —  .     The  current 

/  F 

is  then  given  by  the  equation, 

C  =  -      _  *  ______ 


Capacity  and  inductance  may  be  used  to  neutralize  each  other. 


If  L  — 


,  they  exactly  balance,  and  the  circuit  becomes  non- 


inductive. 


CHAPTER  XXI. 

f  Cells, 
I  Lamps. 
EFFICIENCY?  \  Motors. 

|    Transformers. 
(_  Dynamos. 

Cells. — By  the  "  efficiency  "  of  a  cell  is  meant  the  strength  of 
current  it  will  maintain  through  a  given  resistance,  which  is,  of 
course,  dependent  on  the  E.  M.  F.  and  internal  resistance  of  the 
cell,  the  rate  of  polarization  and  recovery,  and  also  the  "  endur- 
ance "  of  the  cell. 

These  measurements  can  be  conveniently  made  in  the  follow- 
ing manner  :  the  cell  is  joined  up  in  series  with  a  resistance, 
such  as  five  ohms,  and  a  key.  Across  the  terminals  of  the  cell 
is  also  joined  a  Weston  voltmeter  with  low  reading  scale.  The 
method  is  the  same  as  that  previously  described  for  the  measure- 
ment of  battery  resistance  by  fall  of  potential,  and  the  connec- 
tions are  shown  in  Fig.  49.  The  voltmeter  reading  is  first  taken 
with  the  key  open  ;  this  gives  the  E.  M.  F.  of  the  cell  dv .  The  key 
is  then  closed  and  the  readings  observed  ;  this  gives  the  potential 
difference  dz  across  the  external  resistance  R.  The  internal  re- 
sistance of  the  cell  can  then  be  calculated  from  the  proportion, 
4  :  4  -^  4  : :  #  :  X. 

The  cell  is  left  on  closed  circuit,  and  the  key  opened  just  long 
enough  to  observe  the  E.  M.  F.  at  the  end  of  every  two  minutes. 
It  is  then  left  on  open  circuit,  and  the  voltmeter  readings  taken 
every  two  minute  intervals,  for  ten  minutes.  From  these  data 
curves  of  the  polarization  and  recovery  can  be  constructed,  using 
the  times  for  ordinates  and  the  E.  M.  F.S  for  abscissas.  The  "  en- 
durance "  of  the  cell  can  be  obtained  by  keeping  a  closed  cir- 
cuit through  a  known  resistance  until  exhausted,  and  the  am- 
pere-hours or  watt-hours  calculated. 

In  place  of  a  voltmeter,  a  galvanometer  and  high  resistance, 
or  a  galvanometer  and  condenser  can  be  employed. 

Lamps. — The  efficiency  of  a  lamp  is  the  ratio  of  the  energy 
consumed  to  the  candle  power  developed.  It  is  calculated  in 
watts  per  candle  power.  The  connections  for  the  measurement 
are  shown  in  Fig.  97. 

112 


EFFICIENCY.  113 

In  series  with  the  lamp  is  joined  an  am- 
meter and  across  the  terminals  a  voltmeter. 
The  watts  are  obtained  by  multiplying  the 
volts  by  the  amperes.  The  candle  power  is 
observed  by  means  of  a  photometer.  If  a 
rheostat  is  placed  in  series  with  the  lamp  and  FT(;-  97- 

the  resistance  varied,  the  candle  power  and  watts  per  candle 
power  at  different  voltages  may  be  observed  and  a  curve  of 
efficiency  at  these  different  voltages  constructed. 

The  "life"  of  the  lamp  is,  of  course,  less  the  higher  tlje 
E.  M.  F.  employed.  This  may  be  obtained  for  any  given  voltage 
by  leaving  on  closed  circuit  and  observing  the  candle  power 
after  different  intervals  of  time.  The  efficiency  gradually  de- 
teriorates, and  after  a  certain  time  the  candle  power  diminishes 
to  such  an  exent  that  it  is  no  longer  economical  to  use  the  lamp. 

Motors.  —  The  electrical  energy  given  to  a  motor  can  be  meas- 
ured by  joining  a  voltmeter  across  its  terminals  and  an  ammeter 
in  series  with  it.  The  electrical  horse-power  is  then  given  by 
the  formula  F  H  P  —  vo*ts  X  amperes 

746 

If  a  Prony  brake  is  employed,  the  mechanical  horse-power 
developed  by  the  motor  is  given  by  the  equation 
M  H  p    =  P  X  S  x  R  X  6.28 

33,000 

in  which  p  =  torque  or  pull  in  pounds,  s  =  speed  in  revolutions 
per  minute,  and  R  =  the  radius  at  which  the  pull  is  measured. 

The  efficiency  is  the  ratio  of  the  power  developed  to  the 
energy  consumed  ;  that  is, 

^  -  M.  H.  P. 

Efficacy-      E-H— 

Transformers.  —  By  means  of  the  voltmeter  and  ammeter,  the 
energy  given  to  a  transformer  can  be  measured,  and  in  the 
same  manner  the  energy  given  out  observed.  The  ratio  of  these 
two  values  gives  the  efficiency. 

Dynamos.  —  The  commercial  efficiency  of  a  dynamo  is  the  ratio 
of  the  net  output  to  the  mechanical  power  applied  to  drive  the 
machine.  The  output,  or  the  E.  H.  p.,  can  be  measured  with  the 
voltmeter  and  ammeter,  and  the  power  consumed,  or  the  M.  H.  p., 
by  applying  a  Prony  brake  to  the  driving  shaft.  The  efficiency 
can  then  be  obtained  from  the  equation 


The  dynamo  may  also  be  run  as  a  motor  and  the  measure 
ments  made  in  the  same  manner  as  that  given  above  ; 

Efficiency   =  ^LZ: 
E.  H.  P. 


CHAPTER  XXII. 

f  Field  (3C) 
Intensity  of  Magnetization  (3) 


Permeability  \/*  —  -— 

MAGNETIC 

DETERMINATIONS.  /  3  \ 

Susceptibility  I  ~  I 

Hysteresis. 

Magneto- Motive  Force. 
[_  Reluctance. 

Field  (OC). — The  intensity  of  the  magnetic  force  at  any  place, 
or  the  strength  of  a  magnetic  field,  is  the  force  which  it  exerts 
on  a  unit  magnetic  pole.  The  unit  pole  is  defined  as  exerting 
on  a  similar  pole  at  unit  distance  a  unit  force. 

The  C.  G.  S.  unit  of  field  density  is  the  gauss,  or  one  "  line  of 
force  "  "per  square  centimetre. 

The  determination  of  the  "  horizontal  intensity  "  of  the  earth's 
field,  or  any  other  very  weak  and  uniform  field,  can  be  made  by 
method  of  Gauss.  The  measurement  depends  on  two  observa- 
tions, the  time  of  oscillation  of  a  magnet,  and  the  angle  of  de- 
flection caused  by  its  action  on  another  magnet.  The  first 
observation  gives  the  product  of  the  intensity  of  the  field  (3C) 
and  the  magnetic  moment  of  the  magnet  (911),  or  A  =  971  JC. 

91L 

The  second  gives  the  ratio  of-  911  to  3C,  or  (&  =  _ .    From  these 

CfC 

two  results  the  value  of  either  9)1  or  .1C  can  be  found,  thus  : 
The  value  of  9)1  3C  is  given  by  the  equation  : 


in  which  /  =  time  of  a  single  oscillation  of  the  magnet  inseconds,,: 
K  =  moment  of  inertia  of  the  magnet,  6  —  ratio  of  torsion  of 
the  suspending  thread.     If  the  magnet  be  of  regular  shape,  the 
moment  of  inertia  can  be  found  by  calculation  from  its  weight 
and  dimensions.     The  ratio  of  torsion  of  the  suspending  thread 


FIG. 


MAGNETIC  DETERMINATIONS,  115 

may  be  found  by  observing  the  deflection  produced  by  twisting 
it  through  360°,  or,  if  this  is  small,  it  may  be  neglected. 

The  value  of  — -   is  obtained  in  the    following   manner  :    the 
3C 

large  magnet,  whose  time  of  oscillation  has  been  determined,  is 
placed  at  a  certain  distance  (r  centimetres) 
from  a  magnetometer  ;;/,  Fig.  98,  and  the 
tangent  of  the  angle  of  deflection  y>,  obtained 
either  by  means  of  a  telescope  and  scale,  or  a 
slider  and  sight  moving  directly  on  the  scale. 
For  approximate  work,  the  deflections  of  an 
ordinary  compass  needle  can  be  taken  in  place  of  using  a  mag- 
netometer. The  magnet  is  then  placed  at  a  less  distance,  r',  from 
M,  and  the  angle  of  deflection  ^  observed.  From  these  observa- 
tions the  value  of  is  obtained  from  the  equation  : 

OC 

nil   __  i   r*  tan  <p  —  r'5  tan  ^.l 
jg   ~  2   "  r*  —  r'2 

If  JC  is  accurately  known  in  any  given  place,  the  field  strength 
in  any  other  place  can  be  found  by  observing  the  time  of  oscilla- 
tion of  a  magnet  in  the  two  positions,  then  : 

JC  :  OCr  : :  t'*  :  ft. 

The  value  of  JC  can  also  be  compared  by  suspending  a  magnet 
by  a  fine  wire  and  determining  the  angle  of  torsion  necessary 
to  produce  the  same  deflection  in  the  two  given  fields. 

Strong  magnetic  fields  can  be. measured  by  Verdet's  induction 
method.  In  this  method,  a  small  wire  loop  (of  area/),  con- 
nected with  a  galvanometer,  is  suddenly  brought  into  or  re- 
moved from  the  magnetic  field,  with  its  plane  perpendicu- 
lar to  the  lines  of  force,  and  the  deflection  (e)  noted ;  then 

,TC  =   C  ~,  where  c  is  a  constant  of  the  galvanometer. 

The  resistance  of  bismuth  increases  in  a  magnetic  field  and 
strong  fields  can  be  measured  by  a  determination  of  this  in- 
creased resistance  and  comparison  with  tabular  values  empiri- 
cally determined. 

Intensity  of  Magnetization  (3). — This  is  given  by  the  equation 

magnetic  moment 
volume 

The  value  of  the  magnetic  moment  i)7i  is  obtained  by  the 
method  given  for  3£  from  the  equation 


n6  ELECTRICAL  MEASUREMENTS. 

Permeability  (p). — The  permeabilty  of  any  magnetic  material, 
such  as  iron,  is  the  ratio  of  the  magnetic  flux  (&)  through  the 

/D 

material  to  the  field  producing  it— that  is,  /*  =   _.     The  per- 

5C 

meability  of  iron  varies  greatly  according  to  the  field  strength, 
decreasing  rapidly  as  it  approaches  saturation. 

A  convenient  arrangement  for  the  measurement  of  the  per- 
meability of  small  iron  bars  is  shown  in  Fig.  99.  Within  a 
large  rectangular  piece  of  iron  are  placed 
the  magnetizing  coils  s  s'.  The  bars  to  be 
measured  b  b'  are  enclosed  by  the  coils.  A 
small  coil,  c,  connected  with  a  ballistic  galvan- 
ometer, is  held  in  position  between  the  iron 
rods.  When  one  of  these  is  withdrawn, 
the  coil  c  is  thrown  back  by  a  spring,  thus 
cutting  the  lines  of  force  of  the  field  and  producing  a  deflection 
of  the  galvanometer.  Then  if  N  be  the  total  number  of  lines 

of  force  cut,  or  the  total  flux,  (B  =  — ,  where   A  is   the   area  of 

A 

the  cross  section  of  the  bars  in  square  centimetres.  The  value 
of  N  is  found  from  the  equation  N  —  K  S,  in  which  5  = 
throw  of  galvanometer,  and  K  =  constant.  This  constant  can 
be  determined  by  a  method  similar  to  that  given  for  the  abso- 
lute measurement  of  capacity  and  depends  also  on  the  number 
of  turns  and  resistance  of  the  exploring  coil  c.  It  can  be  de- 
termined by  making  use  of  a  standard  solenoid  and  calibrating 
coil. 

The  value  of  3C  is  given  by  the  equation 

oe  =   4  ~  *  c , 

10  / 

in  which  n  =  number  of  turns  in  magnetizing  coils,  c  =  current, 
in  amperes,  and  /  =  length  in  centimetres. 

The  permeability  of  rings  of  iron  can  be  measured  by  a  sim- 
ilar method.  Upon  the  ring  is  wound  a  magnetizing  coil,  and 
also  an  exploring  coil  which  is  connected  to  a  ballistic  galvano- 
meter. The  deflection  is  then  observed  on  either  making, 
breaking,  or  reversing  the  magnetizing  current. 

The  magnetometer  can  be  used  to  measure  the  pole  strength 
of  long  iron  bars,  when  magnetized  by  a  coil  through  which  a 
known  current  is  flowing,  and  the  value  of  N  found  by  multi- 
plying by  4  TT. 

Susceptibility  (k).— This  depends  on  the  measurement  of  2HI 
and  X,  and  its  value  is  given  by  the  equation  k  =  __. 


MAGNETIC   DETERMINATIONS.  117 

Hysteresis,  or  magnetic  lag,  is  conveniently  observed  by*  the 
following  method  :  two  magnetizing  coils  s  s',  Fig.  100,  are 
placed  near  a  magnetometer  and  so  arranged 
that  no  deflection  is  produced  when  a  current 
is  sent  through  them.  The  bar  of  iron,  b,  is 
then  placed  in  one  of  the  coils  and  the  deflec- 

I  I     I sz.         \A/ 

tions  noted  with  an  increasing  and  decreasing 
current.     From  the   values  of  these  deflec- 
tions and  the  strength  of  current  used,  hysteresis  curves  may  be 
constructed. 

Magneto- Motive   Force,  or   total   magnetizing   force,  may   be 
found  for  a  solenoid  from  the  equation  : 


10 

where  N  =  number  of  turns,  and  /  =  current  in  amperes.  The 
current  is  divided  by  10  to  reduce  amperes  to  the  c.  G.  s.  unit  of 
current.  It  is  evident  that  the  magneto-motive  force  =  "ampere- 
turns  "  X  1.257  (the  value  of  4_JY  The  practical  unit  is  the 

\  io/ 

ampere-turn. 

Reluctance,  or  magnetic  resistance,  since  it  varies  inversely  as 
the  permeability,  also  varies  with  the  magnetizing  force.  Its 
value  for  a  bar  of  iron  is  given  by  the  equation  : 

-h 

in  which  /  =  length  in  centimetres,  an:l  A  —  area  cross-section 
in  square  centimetres. 

The  relations  of  the  magnetic  circuit  are  shown  by  the 
equation  : 

Magnetic  Flux  =  ""'gneto.motive  forcg. 
reluctance 


INDEX. 


PAGE 

Absolute  Determination  of  Capacity 106 

Absolute  Determination  of  Current , 99 

Absolute  Determination  of  Inductance 108 

Absolute  Determination  of  the  Ohm 70 

Absolute  Electrometer 85 

Added  Resistance  Method  for  Measuring  Battery  Resistance 64 

Aerial  Wires,  Insulation  of 53 

Alternating  Currents 95 

Ammeters 93 

Ammeters,  Calibration  of 98 

Aperiodic  Galvanometer . 14 

Astatic  Galvanometer 1 1 

Ayrton  and  Mather  Galvanometer 17 

Balance.  Thomson's 96 

Ballistic  Galvanometer       15 

Ballistic  Galvanometer  Method  for  Measuring  Capacity 106 

Ballistic  Galvanometer  Method  for  Measuring  Inductance 108 

Batteries,  Efficiency  of 112 

Batteries,  Electromotive  Force  of 74 

Batteries,  Internal  Resistance  of » 63 

Bridge  Method  for  Capacity 105 

Bridge  Method  for  Inductance 108 

Cables,  Insulation  of 52 

Cables,  Resistance  of 55 

Calibration  of  Ammeters 98 

Calibration  of  Bridge  Wire 43 

Calibration  of  Rheostat 45 

Calibration  of  Voltmeters  86 

Capacity,  Measurement  of 103 

Capillary  Electrometer 85 

Cardevv  Voltmeter 84 

Carey  Foster's  Method  for  Measuring  Low  Resistance     27 

Cells,  Efficiency  of ....  112 

Cells,  Standard 87 

Condenser  Method  for  Measuring  Electromotive  Force 76 

Condenser  Method  for  Measuring  Inductance no 

Conductivity  Balance  39 

Comparison  of  Standard  Cells  v 76 

Comparison  of  Standard  Condensers 105 

Comparison  of  Standard  Ohms 41 

Current 89 

Current,  Alternating,  Measurement  of *  95 

Current  Balance,  Thomson's 96 

Current,  Direct,  Measurement  of 90 


INDEX.  119 

"O'Arsouval  Galvanometer 15 

Decade  Bridge         36 

Deflection  Method,  for  Measuring  Capacity 103 

Deflection  Method  for  Measuring  High  Resistance 47 

Determination  of  the  Ohm 70 

Difference  of  Potential  Method  for  Measuring  Current 91 

Differential  Galvanometer 15 

Differential  Galvanometer  Method  for  Calibrating  a  Bridge  Wire 45 

Differential  Galvanometer  Method  for  Measuring  Low  Resistance.    ...  33 

Differential  Method  for  Measuring  Current 90 

Direct  Currents,  Measurement  of 90 

Double  Bridge 20 

Dynamo,  Efficiency  of 113 

Dynamo,  Resistance  of 69 

Dynamometer,  for  Measuring  Current 95 

Dynamometer,  for  Measuring  Electromotive  Force 82 

Efficiency,  Measurements  of 112 

Electrolytes,  Resistance  of 65 

Electrometers  81 

Electromotive  Force 73 

Electromotive  Force  of  Alternating  Currents,  Measurement  of 81 

Electromotive  Force  of  Batteries  and  Direct  Currents,  Measurement  of..  74 

Electromotive  Force,  Standards  of 87 

Electromotive  Force,  Very  High.  Measurement  of 84 

Electromotive  Force,  Very  Low,  Measurement  of 85 

Electrostatic  Voltmeter 81 

Energy,  Measurement  of 100 

Kail  of  Potential  Method  for  Measuring  Current 91 

Fall  of  Potential  Method  for  Measuring  Low  Resistance 25 

Fall  of  Potential  Method  for  Measuring  Resistance  of  Batteries 64 

Fall  of  Potential  Method  for  Measuring  Resistance  of  Incandescent 

Lamps,  Etc  ..    68 

Faults,  Localization  of 58 

Field,  Magnetic 114 

Figure  of  Merit  of  a  Galvanometer . .  8 

Galvanometers 8 

Galvanometer  Resistance,  Measurement  of 39 

High  Electromotive  Force,  Measurement  of 84 

High  Resistance,  Measurement  of 46 

High  Resistance  Method  for  Measuring  Electromotive  Force 74 

Hysteresis 117 

Impedance in 

Incandescent  Lamps,  Resistance  of 68 

Inductance 108 

Insulation,  Measurement  of 49 

Intensity  of  Magnetization 115 

Localization  of  Faults 58 

Loop  Test 55 

Loss  of  Charge  Method  for  Measuring  Insulation 5a 


320  INDEX. 

Low  Electromotive  Force,  Measurement  of 85 

Low  Resistance,  Measurement  of I9, 

Magnetic  Determinations 1 14 

Magneto-Motive  Force n^ 

Mance's  Method  for  Measuring  Battery  Resistance 65 

Medium  Resistance,  Measurement  of. 28 

Motors.  Efficiency  of II3. 

Multicellular  Electrometer. 82 

Ohm,  Determination  of 7o 

Ohmmeter ' 68 

Permeability 116 

Post  Office  Pattern,  Wheatstone  Bridge  34 

Potential  Difference  Method  for  Measuring  Current 91 

Potential  Difference  Method  for  Measuring  Low  Resistance 26 

Potentiometer  Method  for  Measuring  Capacity 105 

Potentiometer  Method  for  Measuring  Electromotive  Force  76 

Potentiometer  Method  for  Measuring  High  Resistance  46 

Potentiometers b 31 

Quantity,  Measurement  of 101 

Reluctance  117 

Resistance,  Measurement  of 19 

Rheostat,  Calibration  of  . . 45 

Rowland  Galvanometer 1 8 

Secohmmeter  Method  for  Measuring  Inductance 109 

Sensitiveness  of  a  Galvanometer 8- 

Slide  Coil  Bridge 31 

Slide  Coil  Bridge  for  Measuring  Capacity 105 

Slide  Coil  Bridge  for  Measuring  High  Resistance 46 

Specific  Insulation 50 

Specific  Resistance 38 

Standard  Cells  87 

Standard  Cells,  Comparison  of 76 

Standard  Condensers,  Comparison  of 105 

Standard  Ohms,  Comparison  of 41 

Susceptibility 1 16 

Tangent  Galvanometer 10 

Tangent  Galvanometer,  Absolute  Measurement  of  Current  with 99 

Thomson  Balance 96 

Thomson  Double  Bridge 20 

Thomson  Galvanometer 1 1 

Thomson's  Method  for  Measuring  Galvanometer  Resistance 40 

Thomson's  Method  for  Measuring  Capacity • 105 

Telegraph  Lines,  Resistance  of 55 

Varley  Potentiometer 33 

"Weston  Voltmeter 79 

Wheatstone  Bridge . .     a8 

Methods  for  Measuring  Capacity •. 105 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
This  book  is  DUE  on  the  last  date  stamped  below. 


OCT   191947 


27fen<SOi 


LD  21-100ra-12,'46(A2012sl6)4120 


